Hi,
Most transfer switches are wired to be 'off' most of the time, and only energized while the generator is running, say only about 5,500 hours for the life of the motorhome.
So use the 'shore' wire input to the transfer switch from your inverter if possible, so that it will not consume valuable inverter power while on the inverter and battery power. Then when on shore power, the shore or generator power will provide 'unlimited' shore power to keep the 10 watt transfer switch energized.
The relays can run hours at a time without damage. We have indoor fans at my work that run 24/7 for weeks at a time, nearly the whole 8750 hours per year, and at 15 years old they are not worn out. In fact a contactor that is energized for 6 weeks at a time, and only off for a few minutes while the belt is being checked sees less 'on-off' cycles than the compressors, that might cycle on and off 5 times a hour, and only run 30 - 75 minutes at a time in the summer, as little as 10 minutes at a time in the spring and fall. After 14 years of that kind of service, the compressor contactors are showing signs of wear (sparking pits in the contacts from energizing and going off several times a day) while the indoor fans look shiny (less amperage and only typically turn on once in the morning and off at around 11 pm!).
Good luck!
Fred.
