Maybe it doesn't cycle because the car doesn't get cool and the system thinks it needs more cold, so it keeps the compressor on. Just a guess. I'd go after the vent mix door, I think it's letting in too much warm air.
Or I could be all wrong, maybe you are low on frion and it trying to work to get more cold in the car. I know that if the frion gets low enough, it will not allow the compressor to run.