Don't you have to save it in some form before you shut the computer down or you lose power to your computer? Or does Elements save it in some sort of a temporary file.?
It was just that the OP asked about during editing.
"when you are using the various tools in say Elements, does your picture continue to lose detail as you use the program?"
NO it doesn't, as you use the program.
You can save and save and save and save, even make (and save) 99 versions, Control-Z and re-edit, and save that version. Resize, and revert. You lose nothing except the first decompression. That was the question, that's my answer.
Yes of course if you close and reopen, the image will degrade with each version. A smaller image will show the negative effects and pixelation even more than a larger image. Not only soft, but color is lost.
Open and save as a TIF, you now have a master file TIF version. I don't know how many times you can open and save and re-open a TIF before it shows degradation? It doesn't. BUT creating the TIF already introduces some data loss, because the photo is processed vs a RAW which is the Raw data, without color information or processing.
The flaw in the "make a TIF and you can edit that all you want" theory is, creating the TIF loses some data initially as it ads the color data.
Meanwhile:
"when you are using the various tools in say Elements, does your picture continue to lose detail
as you use the program?"
NO - not as you use the program. Only when you save and then re-open that saved file.