Some thoughts on what you may see? Yes, it is often good to have the engine running when moving slides or jacks. Not that is HAS to be running as those items work off the battery. But the idea is that those two items are heavy power users and it is just better if they have all the battery power they need to let them work better without heating.
But then it may definitely be a problem with wiring making good contact to power the controls and motors to move the slide. You may be totally correct that the switch is the problem. Maybe worn or maybe just needing some contact cleaner to clear that as an issue?
But there are a couple other things to consider and one may be easier to change out a plug in style relay than to try to work with finding if a switch is hit and miss?
This is a drawing of part of that.
View attachment 1943727
This relay may be somewhat easy to reach in the electrical box? If not sure where that is, tell us which 2007 view floorplan and we can do a check for that location, if needed?
But the idea may be that when you hit the switch, that may be failing to pass the signal OR that signal may leave the switch but the relay it should move may be at fault!
Two ways to sort the question may help. One is that this relay is a pretty common, relatively cheap item and you might want to just replace it as a quick try?
Second method may be to feel the relay to see if you can feel it move when the switch in front is pressed?
A bit higher tech move is to monitor the power into and out of the relay to see if it is passing that on to the slide motor?
I think I know this little relay and they often have drawings on the side to show which contacts open and close (meet?). That might let you go the higher tech route if that fits.
When you say it works and then doesn't, that makes me jump to contacts that close or not as they should!
There is also the plug that I circled and that can sometimes be helped if we spray contact cleaner on the connections. It rarely hurts anything and may help iof that is part of the problem. I feel that is less likely to be the hit and miss type but getting good power passed on to the motors can never hurt!
With me that move depends on how much trouble to get it found and cleaned!
This drawing is for one of the 07 view and likely is the same as what you have on this section of wiring, so may help to find the relay location and if wanting to change, it also shows the Winnebago part number.
Last page, bottom right for relay info!
However, I think you may be able to walk this relay in to lots of auto parts stores and find they can match it?? I find that is often easier and better pricing than OEM numbered parts!