The tweet says "a tower site" which implies they have others. It's entirely possible/likely that they have multiple towers for better coverage; if one went down they would lose some coverage area but not all of it.

It's an AM station, so they may also shut down overnight (as many small stations do to avoid over-propagation).

Off topic: I could have guessed that guy was a radio station manager without any context. There's just a look to them.