Every day, the frustrations of New York City subway riders spew out in the form of 2,500 often profanity-laced tweets directed at the Metropolitan Transportation Authority.

“Thanks @MTA for making sure we can’t buy metrocards AGAIN,” wrote @itzMzLori, 31-year-old beauty blogger Lori Tenn, who found her card machine closed. “I swear I f—ing hate y’all.”

The job of taking this vitriol—and offering measured responses—falls to the social-media team behind @MTA and @NYCTSubway. The two Twitter accounts for the agency that manages the New York City subway, bus and commuter rail system have more than two million often angry followers.

“We’re New Yorkers, we have thick skins, but we’re human,” said Molly Washam, an even-keeled 30-year-old. “We do sometimes gather around the monitor to see the meanest thing someone could come up with that day.”

The MTA’s social-media team works at a round-the-clock rail control center in Manhattan, surrounded by screens showing train service information in real time. Photo: Erin Lefevre for The Wall Street Journal

To stay calm, she said she does yoga, and recently tried a pottery class.

Rampant subway delays and breakdowns in recent years are making the work more intense. A 2017 report by the New York City comptroller found weekday subway delays rose 83% between 2013 and 2016. The agency has begun a modernization plan to make improvements, including upgrading the signaling system and hiring more subway workers.

New Yorkers’ response to repairs? “Really @MTA, More of your Bs complications,” wrote @MattMercadoNYC, rider Matt Mercado, 34, of the Bronx. “You pick Thursday AND Friday for these ‘Required Repairs’??!?”

“We know they might not mean everything they’re saying,” said Sarah Meyer, the MTA’s customer-service chief. But, “I can’t personally change the signaling system.”

Running social media for any company involves responding to complaints. But the MTA’s team is in a particularly challenging position—facing the combination of generally blunt and often foul-mouthed New Yorkers; an ailing transit system they have little control over; and Twitter, which doesn’t always bring out people’s kindest sides.

“They are a pin cushion for people to take out their anger,” said Karen Kessler, a communications consultant and crisis expert, “and they have limited tools at their disposal besides a thesaurus for 15 ways to say ‘Sorry, we’re working on it.’”

The social team sits in a 24/7 rail control center in Manhattan, surrounded by screens showing train service information in real time. Speakers crackle with updates on police or fire activity, and station managers, engineers, technicians and other subway staffers supplying information are within earshot.

Steven Leonard, one of the MTA social staffers, said he has come to know “the regulars.” “One person [I recognize] can just tweet us ‘where’s my train,’ and I already know this person is somewhere around Howard Beach waiting for a northbound to Manhattan,” said the Queens resident. “You just gotta reassure them.”

Steven Leonard, one of the MTA social staffers, said he has come to know the tweets of ‘the regulars.’ Photo: Erin Lefevre for The Wall Street Journal

Mr. Leonard, an F-train commuter, said he can understand where riders are coming from when they ask what’s the holdup. “If the train’s coming at 8, and it’s 8:05, I won’t stress,” the 30-year-old said. “If it’s 8:30, I might call over here to see what’s going on.”

The flow of tweets has ballooned since the MTA installed wireless internet underground, giving the city’s five million daily subway commuters the opportunity to gripe in real-time. And a new subject: “@MTA WiFi sucks. Waste of money. #rant,” reads a March 11 tweet.

Track work is a favorite subject of commuters’ tweets. Photo: Matthew Rose/The Wall Street Journal

When @NYCTSubway tweeted on Monday that N, R, Q and W train service had resumed after a delay, a commuter responded: “ ‘Resumed’ a phrase which here means, ‘back from terrible to regular old bad.’ ”

Twitter users said they were surprised to get personalized responses. “It was generic, but at least somebody is reading,” said Ms. Tenn, the blogger complaining about the card machine, of the MTA’s polite response to her tweet. (“Good afternoon, Lori. We are sorry for the trouble.”)

The team responds to ask tweeters for train numbers and more information to follow up on certain problems, such as when the air-conditioning isn’t working or when a control panel appears to be dangerously flapping open.

An occasional compliment for a kind conductor or a nice ride “definitely helps keeps us going,” said Ms. Washam, a Brooklyn resident. Actress Jill Hennessy of “Law & Order” tweeted in April about an MTA conductor who smoothed over “an escalating verbal altercation” on the train. “As I left for my stop, had 2 thank him & say ‘God bless,’” she wrote.

“Hi Jill,” Ms. Washam wrote back. “We’re so glad to hear this.”

The @MTA team isn’t above feeling annoyance. “They mock us…Once I mentioned ‘witch’ instead of switch, it just went viral,” said Annie May Morrison, a Bronx resident. “But at the end of the day you assist the customers.”

She was relieved on Wednesday because there was “nothing outrageous or any cursing at us,” she said. When she checked her @replies, a tweet read: “@MTA your app sucks.”

“Today was a good day,” she said, knocking on her desk.

Write to Mike Vilensky at mike.vilensky@dowjones.com