I believe it is the same problem many experience with self-cleaning ovens because we often have had it happen then. Failure after self-cleaning is caused to a thermal fuse blowing because the appliance overheats due to insufficient internal ventilation/cooling of the electronic controls, in which case the blown fuse must be replaced ... they do not auto-reset upon cooling. (One brand apparently has a thermal breaker instead of a fuse, which can be reset by pressing a button on the breaker but that still does not happen automatically.)

Your problem likely is the control panel or main board behind it is breaking down upon exposure to thermal stress and/or humidity, then it "recovers" upon cooling/drying. Could be an erratic component on the board or bad solder joint.

It is also likely to be exacerbated by your broiling with the door open letting the heat broil the control pad. Broiling is supposed to be a closed door operation in all modern ovens.

I have ge profile double ovens about 5yo, I self clean regularly and they work flawlessly. I broil with the door closed though.

Thanks for the info on why the problem, but I really wanted to know if there is a brand/model that doesn't have it. I want to use self cleaning in the existing cabinet. And I will follow instructions about how to broil. I am looking for a viable replacement for the existing oven if it finally conks out for good.