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Neither snow nor rain, sure — but even the US Postal Service is having trouble persevering when it comes to the coronavirus.

Some Manhattan residents served by a Greenwich Village post office told The Post on Monday that they haven’t received their mail — including medicine and checks — for the past week thanks to the contagion taking out much of the center’s staff.

“I went over on Friday, I walked over there, I’m 86 years old,’’ said Leila Mustachi, who lives about a mile from the post office at 201 Varick St.

“They said a third of their work force is out — a lot are out sick — and they couldn’t tell us anything,’’ she lamented. “They said the mail was sitting around in bins and it hasn’t been sorted, just laying around, and they don’t know when it will be ready.”

She and other older residents fretted about being late on their bills, which they receive and pay by mail.

Lou Bullock, an 87-year-old local veteran, said, “I normally get my medicines and my vitamin supplements.

“I haven’t gotten anything’’ since last week, he said.

Resident Marlene Nadler added, “It’s a really bad situation. People are not getting checks or medicine that goes by mail.”

She said that when she recently called the post office, they said only nine out of 61 employees are working because of illness or they have to take care of family members, such as their children.

A worker at the office told The Post on Monday, “We try to deliver mail every day. We welcome people to come pick it up.

“We don’t have the manpower right now. It’s a national emergency.”

By early afternoon, there was a line of 12 to 15 customers trying to pick up their mail.

“I said, ‘Well, it can’t be five days in a row that nobody is sending me junk mail.’ I’m expecting a check, so I came down here to find out what was wrong, and they said, ‘Get in line,’ so that’s what I’m doing,” said Melinda Bruno, 65.

Evelyn Polesny, 48, said, “I didn’t realize we were going to have to stand there in that enclosed space with no air ventilation for 15 minutes. … I feel like it turned out to be a very unsafe situation.”

But local businessman Arthur Curcuru, 38, said of the postal workers, “I understand. They’re humans, too.

“Everybody’s scared. … It’s frustrating I had to come here, but people are sick, so I get it.”

Some residents are pleading with their local pols, including US Rep. Jerry Nadler and state Sen. Brad Hoylman, to help alleviate the mail-delivery hold-ups.

“It’s a tough situation,” Hoylman told The Post. “We understand postal workers are on the front lines, but this needs to be resolved, because what’s worrisome is the very people the federal government is telling to stay home are many of the individuals who depend on the mail in this kind of crisis for their financial and medical well-being.”

A rep for Nadler said USPS officials acknowledged there is a “severe staffing shortage” at the West Village office and promised to send workers over from less busy sites to try to get the mail back flowing.

A USPS spokesman told The Post in a statement, “The Postal Service continues to flex its available resources to meet the local workload on a day-to-day basis.

“We thank our customers for their patience, and our employees for their efforts, in these unprecedented days.”