PLEASANT HILL, Calif. — Bonnie Ronk is something of a public health matriarch at the Mt. Diablo Center for seniors in this liberal Northern California suburb.

When Ms. Ronk, a great-grandmother whose red walker bears a sticker saying “El Jefe” (The Leader), tells her peers to pull their masks over their noses, they oblige. When she received both doses of the Covid vaccine and a booster and told others to do the same, they did.

But even Ms. Ronk, 79, has not gotten the latest Covid booster, which was updated to protect against the Omicron variant and has been available since September. She said she didn’t know about it.

Across the United States, where about 94 percent of people 65 and older had their initial Covid vaccines, only 36 percent have received the updated shot, known as the bivalent booster, according to data from the Centers for Disease Control and Prevention. Seniors have offered an array of explanations: They were unaware of it, unable to find it or unconvinced of its value.

As the pandemic barrels into its third winter, and Covid hospitalizations and deaths climb once again, medical experts worry that there is no effective plan to update the immunizations of the most vulnerable Americans. Two years ago, when Covid shots were first introduced, the federal government sent teams into thousands of nursing homes and community centers to vaccinate seniors, curbing the devastation of the virus.

But so far this fall, the White House has only offered grants to community organizations to get shots into the arms of older people, without the clear messaging strategy or logistical support that they need most, many caregivers and nursing home executives said in interviews.

“The governmental and philanthropic support feels nonexistent,” said Debbie Toth, the chief executive of the nonprofit Choice in Aging, who helped bring thousands of the initial vaccines to adult care facilities and housing complexes in the East Bay of California in early 2021.

The diminishing immunity of seniors has largely transformed the Covid pandemic in the United States from a threat against the unvaccinated to one against the old, many of whom were once well protected. People over 70 are being admitted to a hospital with Covid at a rate four times higher than that of the general population.

The most recent available death counts by age showed that almost 90 percent of Covid fatalities were among people over 65.

“The evidence is clear: Even if you got the shot two years ago, your immunity has waned. But the people who most need to hear that have not,” said Dr. Michael Wasserman, a geriatrician and the public policy chair of the California Association of Long Term Care Medicine. “When you combine pandemic fatigue with no real plan from the government together, what we have is a perfect storm.”

The Biden administration’s Covid plan for the winter includes $125 million in grants to two community organizations, USAging and The National Council on Aging, for programs to vaccinate older Americans — a far less direct approach than when it dispatched CVS and Walgreens workers into care centers after the first shots were authorized. The plan also includes letters to governors encouraging more nursing home shots and a television ad campaign that targets seniors in racial and ethnic minority groups.

Mary Wall, the chief of staff of the White House Covid response team, said the administration was doing what it could with the limited resources available, but acknowledged that this time, the administration was relying on states to shoulder more of the burden.

“We’re really instead asking them directly, please go and host on-site clinics,” she said.

She called the grants “a great start,” but stressed that a more robust financial investment would require cooperation from Congress, which has repeatedly refused President Biden’s request for an additional $10 billion in health funding, a vast majority of it for the coronavirus response.

“Realistically,” she said, “this is not something that we have gotten more money for, for a while, despite repeated asks to Congress. We’ve been trying really hard to look with great sobriety at our resources.”

Epidemiologists agree that among all pillars of a national response, widespread vaccination is among the most valuable. They estimate that Covid shots prevented 650,000 hospitalizations and 300,000 deaths among seniors and Medicare beneficiaries in 2021 alone.

But the virus has since evolved, and the original vaccine formula is no longer a good match for circulating variants, a particular danger to seniors with weakened immune systems and underlying conditions like heart disease and diabetes.

Even the bivalent shot has limited ability to prevent infections from the latest Omicron variants, but it is very effective at preventing serious illness and death. According to C.D.C. data, people 50 and older who received multiple boosters had half the risk of dying from the virus than those with just one booster.

Dr. Sabine von Preyss-Friedman, a geriatric specialist and the chief medical officer of Avalon Health Care Group, said the apathy among some seniors reflected a misconception about the vaccine’s purpose.

“People are thinking, ‘I got the shot, and I still got Covid, so what’s the point?’ They aren’t thinking about the fact that they got Covid and lived.”

As part of the federal push, the Centers for Medicare and Medicaid Services also added a recording about the vaccine to its 1-800-MEDICARE line and sent emails to newsletter recipients “to share information on these updated vaccines, including when and how to get them.”

But a recent survey by the Kaiser Family Foundation, a nonpartisan research organization, found that 40 percent of people 65 and older said they had heard little or nothing about the new booster. About half of homebound Americans 70 and older don’t have a computer, according to surveys, and more than half have not used email or the internet in the past month.

Contra Costa, the East Bay county where the Mt. Diablo Center operates, hasn’t experienced the politicization that has turned many American communities against public health measures. Here, front yards are still dotted with signs praising health workers. A 14-row parking lot has been repurposed for drive-through Covid testing.

Posters in every walkway encourage six feet of distance. The center’s mascot is a stuffed pig in a rainbow cape wearing a miniature mask. “Not all heroes wear capes,” a sign declares, “but they do wear masks.”

Yet even at this facility, where 100 percent of participants received their initial vaccines, only 40 percent have gotten the bivalent booster. At Pleasant Hill Post Acute, four miles south, every resident received the original shots, but only one in five is now up to date. At Vacaville Convalescent and Rehab, just north, almost 90 percent of residents were vaccinated, but 13 percent are up to date. Seven residents there tested positive for Covid last week.

Ms. Ronk has a chronic inflammatory lung condition that puts her at risk of severe Covid. She said she liked to stay “as healthy as I can,” country music blaring as she exercised in the center, using plastic water bottles as dumbbells.

She would have been “darn glad to get it,” Ms. Ronk said of the bivalent booster, had she known about it.

Alexandr Makedonsky, 84, a former denture technician who considers himself “very pro-science,” said he eagerly sought the initial series of Covid vaccines and two boosters after a friend was hospitalized with the virus. He didn’t know the fifth shot was better suited to Omicron.

Part of the problem, according to Alex Stoia, a nurse at the facility, is that the eligibility criteria for the new vaccine was not straightforward.

“I can’t tell you the number of people who asked whether they should wait longer for the bivalent, since they’d just gotten a different booster in September, and we didn’t know what to tell them,” she said. “Even the people advising me couldn’t figure out the recommendations.”

Logistics are also a mammoth challenge. Ms. Stoia, who manages care for homebound seniors, said taking them to vaccination clinics can be nearly impossible: They may not hear the phone ringing; there’s nobody to help them get dressed; it’s too cold to wait on the curb for the van and, when it arrives, the electric wheelchair often doesn’t fit.

In Los Angeles County, where an estimated 500,000 residents are homebound, the public health department said it sent only eight nurses to provide in-home vaccinations each day.

“They need to understand that you can’t just tell people to get the vaccine, you have to bring the vaccine to the arm,” said Ms. Toth. “And trust me, that last mile is the hardest.”

To many public health experts, the most difficult-to-teach seniors are those who doubt the new vaccine’s worth. New survey data from the Kaiser Family Foundation showed that about one-third of adults 65 and older who received the original series of Covid vaccines but not the booster said they didn’t think they needed it, and a similar share said that they didn’t think its benefits were worth it.

Dr. Noah Marco, chief medical officer of the senior care nonprofit Los Angeles Jewish Health, said he “continues to be amazed” that the federal government has not enlisted marketing experts to “create updated messaging that actually works.”

“Coca-Cola spent billions of dollars over decades convincing us that we need to be buying and drinking bubbly water with sugar and caramel in it. Come on, is there really nobody around to lend a hand here?” Dr. Marco said.

At Mt. Diablo, the 51 seniors who still haven’t received the updated shot could use a fresh pitch. Two friends, Tsilya Tankover, 95, and Faina Gutkin, 77, got their initial vaccines, but they are among those refusing the booster that fights Omicron.

“I feel fine,” Ms. Gutkin said, pushing around the collard greens on her plate as she shared plans to go tango dancing. “Why do I need it? I’m still waiting for someone to tell me that.”