This sounds like a freon problem, it sounds like your getting thermo expansion valve freezing due to low volume of freon in your system. If you have a set of gages you should be able to see whats happening when the system isn't blowing cold. if the low side drops during this part its your freon expanding too soon in the evaporator coil from low volume, but still enough near the right pressures to keep your low and high switched from tripping.
At this point your sensor bulb at the end of the evaporator coil freezes close due to the fact the freon isnt changing state at the right point (at the end of the evap coil)and your getting too much gas/liquid at the bulbs location.
Since the system will still try to run the your best bet here is to run down to your local automotive shop and have them evac your system and throw in the right volume, now measured in weight/ pounds.