Yeah. The only AI that [i]could[/i] have survived is Cortana, as she was the only smart AI made by a living duplicate (illegally made) of doctor Halsey's brain. Another duplicate could have been made, or a sacrifice of Halsey's brain itself, and used to rebuild her neural networks, extend the lifespan, or reroute her personality files to a previous, calmer state. This also had the disadvantage of many risks, one such one being a new Cortana being made instead of a repair of the old.

The only AI to live far past the deadline is Juliana, an insurrectionist AI stationed on the rubble. The only reason she lived is because she was given very complex tasks, and things she really had to pay attention to.

There are ways that AI can survive rampancy, however these are purely theoretical or they just extend the lifespan (an example being Mack and Loki, whom would continually switch command of Harvest's AI data center).

A more complex discussion to Rampancy can be found [url=http://www.halopedia.org/Rampancy]Here.[/url]