Here's a surprising update after talking with Winnebago and Parallax Power, the manufacturer of the transfer switch:
Winnebago agreed with my diagnosis that there was a problem with the transfer switch. Since the switch has a two year warranty, the rep recommended that I call Parallax. I did and spoke with a tech support rep there. His response was that their transfer switches are not designed to be powered while driving the coach. Because they are generator priority switches, when the generator is running, the contacts are held together with the relay. According to Parallax, there is no way they can design a relay that will remain closed during all kinds of road conditions. They won't replace it and cannot confirm that a replacement switch won't have the same problem, which they said exceeds their design requirements.
When I called Winnebago back, the rep was surprised by Parallax's response. He suggested that if this was common with their switches, he would have heard about it. I asked for a recommendation for a switch that was intended to be used while driving and he told me that Winnebago only uses Parallax switches. He suggested that I replace the switch, but I have a real problem with that. Why would I buy another transfer switch that the manufacturer says shouldn't be used. If it does the same thing, I will be the proud owner of two shoddy switches!
Apparently, Winnebago is installing transfer switches that are not intended to be energized while the coach is under way. I don't recall reading this in their manual and I don't think the guy that did the predelivery inspection mention that I should use the generator while moving, like I have done with my other two motor homes.
I have written an email to Parallax and copied Winnebago asking them to confirm what I was told. If this is true, everyone with a Winnebago coach should look into this and make sure you're not encountering the same problem. The only reason I know about it is because I added a roof air conditioner. With only basement air and road noise, there is no way most people would be aware that it was occurring. Constantly cycling the compressors on and off puts an awful lot of wear and tear on them. If Winnebago doesn't recommend to not use generators while under way, should they be on the hook for electrical system damage that is caused by this?
I don't know about you, but to me this is a BIG DEAL! I live in Texas and if I can't run the generator on the road, Winnebago needs to put a whole lot more resources in the dash air. When it's 100 degrees out, a handful of vents on the front isn't going to cut it. For now, I am leaving the switch wired backwards.
Winnie owners may want to give them a call to get position on this.