When trap doors are up (open) you press a button and the trapdoor will go to the down (closed) position. They will not come back up.
So,
[] = Button
[-] = Open trap door
[=] = Closed trap door
First:
[]
[-]
when you press the button the trap door goes into:
[]
[=]
and won't pop back up into it's open position
Do you mean it stays closed when you press the button again after that?
Applying power to a trapdoor should make it open, removing power should make it close. So pressing a button over an open trapdoor will make it shut once the button depresses.