Well, it definitely remembers the level position or you would have to re-establish it each time you put the batteries back in - and what would be the point of that?
As LHaven said, it's would be stored in flash memory. Most microcontrollers (which is the brain inside the control board) would come with flash memory built-in, so it's easy to implement from a design point of view.
I honestly don't know if it doesn't also remember the hitch position, but it wouldn't surprise me either way.