Wanted to make a thread because I was experiencing the same issue and found a way around it. This occurred at Cathair Chomain in Ireland and the symptoms were that my army would not respond to commands initially - the enemy rushed me while firing arrows and random troops, usually infantry, would go up to meet them in 1s and 2s, there usually being 5-8 of my infantry fighting them at any time.
However, after a certain number of the enemy died, my army immediately charged the gates and began to hack at the door. The siege engine wheeled up to the door but did not knock it down. In one instance the siege engine caught fire, or maybe the door caught fire first but either way the door started displaying these fire graphics. I waited for 10-15 minutes but the door never fell so I reloaded again.
Eventually my troops killed the enemies that sallied out from the castle, rushed up to the castle doors for them to not open again, but I ordered them to follow me up the ladder. The pathing was very buggy in having them come up the ladder but I found that if you play around with it you should be able to find a spot in which they'll follow you. Initially, standing right in front of it works, but then you need to move over to the stairs.
Eventually I worked my way around the entire top of the castle ramparts counter-clockwise along with most of my army, marched down the stairs and charged them at the enemy. Finally won the battle.
In another siege at some other castle the doors burst open but 100 or so of the enemy - 50 for each door - got trapped BEHIND the doors. It took forever for my troops and them to slash at the doors with little pieces of their swords coming out to finally finish off the enemy.
Sieges really need some attention paid to them guys. Brytenwalda is fun but I'm gonna try Prophesy of Pendor and see what that's like. I'd like to play a less buggy mod. This is a fabulous one though, just improve it where and when ya can. Thanks for the hard work!