It probably needs to have the condenser cleaned out. They get packed full of lint and dirt and the unit will stop cooling. Your landlord will probably not want to do that since the whole unit will have to be removed to get at it.
I think that will eventually cause a compressor failure. Some units have a high pressure cutoff switch which will trip when the head pressure gets too high, to protect the compressor. But a thru-wall unit probably does not, so it'll keep running with excessive high head pressure, which will eventually kill the compressor.
So a landlord who knows about air conditioners will realize that (1) he can pull it to clean it out now or (2) pull it to replace it with a new one later.