Ensure you're playing the latest version of the game. Check for updates on your platform of choice (PC, Xbox, PlayStation, etc.).
An ounce of prevention is worth a pound of cure. To avoid the door bug entirely: prince of persia forgotten sands door bug fix
If the above fails, the door is truly locked. You need to bypass it by altering your save file. This is the most reliable method for PC users. Ensure you're playing the latest version of the game
Warning: Backup your Saved Games folder first. prince of persia forgotten sands door bug fix
This resolves 90% of cases where a door that should open after a fight or puzzle doesn't.