We had a tornado come through my neighborhood back in Feb, crazy, and we were without power for almost 2 days. I hooked up most lights on my gas powered generator and my GE dimmers didn’t like it and they flickered when they weren’t on 100%. I ended up telling family not to use them as I was afraid of a failure. All of my battery UPS hates the generator too. I did a little research and found others had similar issues at least with gas powered generators. My neighbor has a whole house natural gas powered generator and it produces much cleaner and consistent power.
Depending on the age of your GE switches they do come with a 2 year warranty so you may want to reach out to Jasco support to see what they say.
I have had several ge switches die. The blinking blue led light. In my case it always happens when the power blinks. That said I have also had 2 come back to life after a day or two. Always after a replacement had been ordered.
I would guess your generator may not be a true sine wave output. We had a generac that was not and several electronics items would refuse to run when it was online and I had to buy a power conditioner.
Have you tried turning the breaker off and on to the switches in question? I had this happen to one of mine after a power outage and couldn’t even control the switch manually. It came back to life after cycling the power from the breaker. That was 2 years ago and it’s still working.