I've noticed this problem for a while now. I can be out of combat and the prompt to go through an Imperial City door will not always show up. I often have to walk away from the door and then back up to it several times before I can go through. This wouldn't be as big of an issue if it didn't leave players so open to attacks. Taking the extra 5-10 seconds to try and get the door to work is plenty of time for a player to hit you with elesus from a mile way and keep you in the district.
This door operation is not affected by the stuck in combat bug, which is also present in Imperial City. I can use doors when I have the stuck in combat bug, but not if I am actually in combat.