i keep losing the settings icon from my ipad. How do i get it back and why does this keep happening?

You can’t delete the settings app. If you could, you would essentially render the device useless in many ways. Do a search for it. Swipe down from the middle of any Home Screen and type in Settings in the text field at the top. If you accidentally placed it into a folder, the folder name will also appear in the search,

I tried what you suggested, and of course it found the Settings app, but it did not reveal the folder it was in (after I deliberately moved it into a folder).

I suggest once they find the Settings app, they execute it, go into General, Reset, Home Screen Reset.

Mine is not in a folder, but in the default Home screen location. That user-created folder must be why you see that.

The folder name isn’t an in your face kind of thing. It’s probably a bit too small and can get overlooked. I have a folder for Apple Apps on my iPad and when I searched for Podcasts, this was the result.