Maybe the blower motor resistor is failing when you're running on high for an extended period of time. I've also seen the breaker for the high speed for blower motors get weak and kick out on high speed.
I'm not sure if there's some kind of fail safe that won't let the a/c system kick on if it's low on freon? I'm a heavy duty tech for a living, but just trying to lend a hand. I guess you could check the a/c connections for "dust" build up around them for leaks.