There are so many factors that worsen stability. One of them is your situation in warfare, others like distance may enter this list too. The formula seems not so simple, sometimes it just worsen to a certain point and stops, because all cities start with a base value and are modified by their current situation.
Despotism is the worse civic for it, after a few cities (4 in Deity and Huge, but maybe in other difficulties as well) you're screwed no matter what. You need to get Hereditary Rule ASAP. Under Hereditary Rule you may even combine it with Slavery and run a Massive Empire. I'm playing a MP game with a friend with Hannibal (Fin, Cha) of Carthage Marathon, Huge, Deity. 5 turns to discover Liberalism. My civics: Hereditary Rule, Bureaucracy, Slavery, Descentralization and Paganism (A strange game indeed, India and the Aztecs discovered ALL religions, and we only got contact after Caravels). I'm now with 15 cities, and one of them is really far away from my capital:
Surely Parthian, Tolosa and Vienne should be rebelling, but under Hereditary Rule the stability problem increases at a slow pace, so I'm razing several barb cities that keep spawning in the mid of my big island and after each city conquest it improves my stability situation. Don't worry about worsening, worry about Danger! After Danger you really need to make things better, before it you just need small remedies here and there (city conquest is the best and easiest of all)