Mine both stay up. The one in the front bedroom is on a swing/tilting arm that folds back almost flush to the wall when stowed and has a built in locking thingy to hold itself in place when going down the road.
The only thing I have to remember to do is actually fold it back and make sure that the locking thingy actually does make that little click noise! LOL. Forgot to do that on one trip and found the screen extended out from the wall pretty far when we got it back to the storage lot - but even then there was nothing damaged. I just learned another checklist item for the next trip...
