If a creature is invisible, it has several advantages against creatures that can’t see it: It has total concealment against them, it doesn’t provoke opportunity attacks from them, and they grant combat advantage to it.
Therefore the invisible state itself is not "toggled" by its nature. (Unlike, for example, prone, which offers standing up as an explicit option.)
Therefore, the only rules governing when invisible is active for a given monster are within the monster's stat block.
Duergar Scouts, the little **s have:
Underdark Sneak At-Will
Effect: The scout becomes invisible until the end of its next turn or until it hits or misses with an attack.
On a positive note, they only become hidden if they then take a move action (which is likely, but it means dazed is quite handy.) Unfortunately, the only way to make a duergar scout visible against its will is to kill it or use one of your powers that removes invisibility.