According to the books, you can have a standing invitation. Harry has entered Murphy's house with it's powerful threshold without issues to 'water her plants,' for instance.
I'd play it with the "fun rule" -- if it's more fun for a threshold to be refreshed and require a new invitation, do that. Otherwise allow a standing invitation if it's put that way. The whole "using a threshold as a trap" thing is a moot point, since the threshold itself is what makes the power get left behind. Once you're inside, you're inside, and you can always leave -- the threshold doesn't make you leave your power inside if you try to go out -- it's one way.
