Another reason the gates don't shut is because one of your cavalry (most likely your captain or general) has got himself glued to some piece of siege equipment that he was trying to destroy and is fighting for his life.

Or a unit has stopped routing in the gateway and is awaiting orders.

Or the gateway is so narrow that the unit has bottlenecked and one or more has got glued to the outer wall.

(Pathfinding around gates is notoriously patchy)