Landlord Refusing To Take Rent Money

Location: New York City

Trying to prepare for when this inevitably gets worse. I signed up for automatic payments when I first moved in, but it comes out at random times within the first week of each month. Utility bill and rent came out at the same time; bill went through, rent did not. Added more cash to my account and emailed Landlord asking them to try again and waive any late fee given that 1 I've never been late before and 2 it's hard to estimate when they'll take the money. They didn't respond.

Followed up a few days later and they said I actually owe more money because they fixed the elevator and upped everyone's rent. I'm like, whatever, just take it. They do not.

Call the office and no one answers. Email personal and department contacts, still nothing. I'm getting automatic "settle your account" emails and, when I write back, they won't tell me how, just that I need to do something. There's no online portal and their office is hours away. I work 12+ hr shifts and don't have the energy to keep chasing after them to take my money, so I'm giving up.

Obviously this isn't over, but I'm lost on what to do or how to prepare.

Can they take me to court over this? If so, would I be able to avoid the legal fees after proving I tried for 20+ days to resolve this? Should I be saving the rent money in an account and ignoring it until then? Are they trying to evict me and claim I never tried paying? Are there housing services that deal with scenarios like this that can help me?