frustrated New Jersey with its system, and in late February, after days of website crashes in the nation’s capital, the company admitted it had “fallen short.”

Microsoft said in a statement that it was “focused on helping governments manage their Covid-19 vaccination programs as quickly, safely and efficiently as possible.”

PrepMod’s woes have led to delays in vaccine rollouts in places like Washington State and Pennsylvania. When the vaccine appointment website in Massachusetts went down for several hours after a surge in demand, PrepMod took responsibility and apologized.

Andrew Therriault, a Boston data scientist, said he was “astounded” by the extent of PrepMod’s shortcomings. One problem he found was that the system did not reserve an appointment slot as people filled out their information, so they could be booted out at any time if someone else beat them to that particular slot.

“I try to imagine somebody doing this who’s not so tech savvy — that basically means they have no opportunity to compete,” Mr. Therriault said.

aiming to reach Black and Latino communities that had low vaccination rates issued MyTurn appointment codes to those groups that ended up being shared widely, including among more affluent, white communities. Because the codes did not expire after a single use, those people were able to use them to get vaccinated before it was their turn.

Ms. Tate of PrepMod said health care workers and others who were improperly sharing the links were at fault.

“That’s not a problem with our system. That’s a problem with people who should be responsible,” she said. The company, she said, has added an option for unique links.

Salesforce declined to comment, but Darrel Ng, a California health department spokesman, said MyTurn had also added unique links.

forcing the site to close for several days because it ran out of doses.

“The MyTurn system is fraught with issues,” Dr. Ghazala Sharieff, Scripps’s chief medical officer, said. “These challenges are adding another layer of unnecessary stress to our team.”

Health officials said the reliance on outside companies’ imperfect tools underscored the need to invest in technology for public health departments, many of which still use paper and fax machines to keep records.

State registries that keep track of residents’ vaccination histories — known as immunization information systems — could have been adapted to schedule appointments, said Mary Beth Kurilo, a senior director at the American Immunization Registry Association. But the federal government never asked them to, she said, and they would have needed more money and time to prepare.

Some regions have elected to avoid technology entirely.

In Johnston County, N.C., southeast of Raleigh, the Health Department decided it would have been too much of a strain on the staff to manage appointments online, so shots are first come first served.

The policy has been efficient, said Lu Hickey, the Health Department’s spokeswoman, but it means the county — which also does not require in-person identification — does not know whether people are being vaccinated in the proper order and has to rely on the honor system.

In Richmond, Ms. Morrison said officials were searching for solutions and even thinking about trying VAMS again.

“We’re cobbling it together at the local level through a lot of manual effort and workarounds we’ve put in place to put Band-Aids on,” she said.