Background:
SoB Level 68 - Maze of Madness has 3 doors that are only openable by heroes standing on adjacent encounter markers.

There is no restriction mentioned about closing doors.
The general rules for doors always have doors being able to be *both opened and closed* by the same 'group' of figures.

If monsters can shut doors in this level it is possible for the heroes to be unable to progress except by killing themselves (and there is no forward glyph, so that means returning to the start glyph).

Both the tiny room with the treasure in and the final room with the boss in can be locked behind the heroes trapping any inside with no possibility of escape. Arguably getting trapped in the small room is foolish, though a very harsh penalty, but getting trapped in the large room is fairly reasonable as the Leader may be in there and then escape, shutting either door behind himself.

Question:
Q. Can monsters shut the special doors on SoB Level 68 - Maze of Madness?
A1. Yes. There is no restriction on shutting the doors, only opening them. This may lead to a situation where trapped heroes have no option but to kill themselves so they can return to the dungeon through the starting glyph.
A2. No. All references to the ability to open doors also refer to the ability to close doors. Since the monsters cannot open special doors on this level, they also cannot close them.
A3. No. The card for this level should say that the doors may only be opened *or closed* by a hero standing on the adjacent encounter marker.