Yours should have shore power connected through and when the generator feeds power to the transfer switch, a time delay of about 30 seconds allows the generator time to warm up and then the contactor coil is energized and power is then provided from generator through the transfer switch and into the coach.
If it is a Newer coach a Surge Guard may be built into your EMS system and this is normal operation. It may also be why the power dropped out after 20 minutes. If the voltage gets too low or too high, or even a surge can cause the Surge Guard to do it job and protect your coach by disconnecting power.
When the power has been interrupted, and if you are comfortable in checking inside the transfer switch with a volt meter to determine if power is getting through the Surge Guard and if so getting through the transfer switch. These terminals will be marked on the inside of the transfer switch . Remember to use the Neutral from the generator for all Volt Meter readings