Ok, here's another wild guess...
Possible loose connection on the transfer switch/generator circuit, or the generator might be low on oil (or has the wrong weight oil installed) and cuts out for a second. Either way, the transfer switch timing circuit kicks in and power is disconnected for about 30 seconds. In addition, I believe the AC control circuits have timers built in so that if they are shut down with the compressor is under pressure, it keeps the compressor from starting for 2 minutes or so to let the pressures stabilize in the lines.
Do you have something else plugged into the 120VAC outlets you could monitor while travelling down the road? Either a light or radio or something? That way, if you lost power, you'd notice it right away.
I guess it's also possible that a loose connections anywhere in the AC circuits might also cause them to cut out.
But that's just a guess. Do you have any more hints you can send our way?
When they do cut out, you stop and the generator is still running, will the compressors come on after a short while? If the generator isn't running when you stop to check on things, what is causing it to shut down?
In answer to our question about powering down before switching from generator power to shore power or vice versa. YES, you should shut down all of the major current drawing appliances (AC's, electric water heater, microwave, etc.) when switching between power sources. This will minimize arcing on the transfer switch. For a similar reason, you should always have the power pedestal breaker shut off when connecting or disconnecting your shore power cord to minimize arcing at the shore power plug/receptacle.
~Rick