Do you use the menu Help >> Sign out when leaving Elements?
That does not mean you 'log out', that means you 'deactivate' your license for that given computer.
If that's not the source of the problem you'll have to give more details about your OS version and your hardware.
When I leave PSE 14 I close by clicking on the X.
I am using windows 8.1 64 bit, on a Dell XPS 8700 with an I7 processor. It is my opinion that I should never have to log in to use PSE 14 once the initial install is over, where I have to enter a special registration number.