Solving air conditioning refrigeration problems is like going to the doctor. One or more problem may exist.
The unit may simply be low on freon which can cause part of the evaporator to freeze up and cold air stop. This is the most common problem. The expansion valve is not able to do its job without the proper level of refrigerant. Go to a automotive shop and buy a combo that will allow you to put freon in your system and a gage that will tell you if you are low on freon. The low side connector is on the exterior firewall area and the low side connecter is where refrigerant is added. Add freon until the gage reads you have the correct amount of freon. That may solve your problem. With the amount of refrigeration hoses in motorhomes, a small leak is common. Currently, I add a can of freon about every two years. I doubt I can find a leak this small!
The expansion valve may be defective. When you turn on the dash air, the expansion valve opens to its capacity to as quickly as possible pull out the calories inside your coach. As the inside of your coach cools, the expansion valve restricts the flow of freon resulting in a colder outcome as the liquid refrigerant expands quicker in the evaporator with less freon allowed to flow into it. If the refrigerant level is good, anything outside this function, the expansion valve most likely needs replacing.
Another possible problem is the system may have moisture. If not properly evacuated to remove all moisture after the system is open, moisture can be present in you freon. The moisture if not caught in the dryer, may freeze up at the expansion valve stopping the flow of refrigerant. If you have not had any work done to your dash air system that include unscrewing hoses in history, then moisture may not be your problem.
Someone else touched on a problem with the compressor clutch. The greatest load on a compressor is when it is first turned on. Slipping can be heard and visually seen and sometimes smelled. This condition will get worse with system use. Sparks can ultimately fly from a compressor clutch as it scrubs metal to metal and the compressor will not longer turn.
Good luck in establishing your solution.
2003 Alpine Coach
2009 Jeep Wrangler 4-Dr Rubicon