Using A/C for a lager chamber

I think I've broken my second A/C unit doing this. I routed the temp sensor away from the cooling fins and toward the back, and hooked it up to an external controller that kept the temp between 30 and 40 and it ran just fine for about 2 weeks, and then quit blowing cold. This is the second A/C to do this, and I don't know why. It was running for about 5 minutes every hour, so I figured it wasn't perfect, but not bad.

Is there something that I don't know about making a wall A/C cool to 35 degrees?

I know it'll ice up, but I figured the ice would be gone in 30 minutes. Am I wrong? And if the coils do freeze, will it kill the A/C? Isn't the freon mostly unaffected?

If icing is the problem, will it be solved by running the fan constantly?

My understanding of a/c (automotive) is that there are usually 2 reasons for it not to blow cold. Either there is a coolant leak, or the compressor is going bad.