Actually, I see AIs going broke fairly often even at Suicidal, where they get an econ bonus big enough to make colonies break even at about half a billion people. Of course, my trading IP for all their BCs every four turns might have something to do with it
Minor civs tend to get it worst, but I've seen major civs go 12+ turns with negative bc balances.
I have seen them do that too, but never when they are in a dominating position - mostly when they are being munched by an AI in a dominating position!
In my current game, i have drengin set to Godlike and we both have ships at maximum technology. The Drengin are able to maintain a staggering number of fleets compared to me, and most of their planets are dominated by factories wheras most of my planets are dominated by stock markets! I hold a forward position on their boarder with 16 military starbases!! Initially they went for those starbases pretty hard but since i have seriously upgraded the ship support modules, they seem to have given up attacking me and have focussed on other enemies. Thats pretty smart of them really!
My own power fleets can stand toe to to against theirs away from the starbases but the casualties are horrible, so i have started building cargo hull vessels armed to the teeth. They are cheaper and, well if my ships are going to die regardless, they may as well be cargo hulls. Hitpoints and defences are irrelevant to the game when maximum weapons tech is in play, save for 1 on 1 combat.
Anyway, in this game i have seen two drengin fleets dissapear on approach to my forward starbase location? This is odd behaviour indeed, because at least those ships may as well go out fighting rather than just disband? A sign that their finances are under pressure tho..... especially since i put agents on all their farms!! 
