Air conditioner temporarily stops working on long trips

This only seems to happen on very long trips.

You will be driving and the air is working fine. Then you find that it is blow less and less cold air (less volume of air), until finallly you have the fan all the way up (and hear it high), but nothing is coming out. You let the air conditioner sit for 10-15 minutes, and it starts working again, usually for hours.

My thought is that the AC is freezing up, and stopping air flow, then when I shut the air off, it defrosts all of the ice and allows for cool air to flow again.

My questions are:

Am I right?
If so, what can I do to fix it?

I think you are on the right track. Try replacing the low pressure cycling switch by the accumulator.