Am I to understand that a user must remain signed in to use PhotoShop Elements without being constantly prompted to sign in and enter a serial number? That happens whenever I sign out through the menu.
Why are you signing out? Whenever you do, the computer becomes deactivated and you have to sign back in with the serial number for each Elements program on your machine. I'm not sure, but this seems to be a new phenomenon. In the past, I thought that if you sign out of one program, you can remain signed in for another version, but I may be wrong about that.
If you have to sign in with a serial number each time without signing out, take a look at the procedure here.