Certified letter. “The lease which you have with me says that you (through your manager) are responsible for the upkeep of the refridgerator. This is not a matter of being briefly broken and then repaired; they have malfunctioned in _______ ways since _date_. This is a violation of the terms of the lease. Please address this problem promptly or I will be forced to take further action.”
Small claims or calling a city official (different depending on where you are) is the next step

I once had a similar problem to yours, going on for months. I simply threatened to get the city involved. Next day, a repairman showed up. )You can, of course, follow through on your threat, if need be.) No landlord wants to have to deal with a city inspector.