The single cities are eventually removed by the inactive player server sweep (supposed to happen weekly)

Once you get a city down to 15% loyalty, it changes to Public Grievance - loyalty will then drop by 1 pt every 6 minutes or so (even if you stop attacking) and as long as the player doesn't comfort.

Don't forget at 5% loyalty the gates will open and you need to fight any troops held in the city.

NPC loyalty drops continually so just keep attacking to conquer.