Felix was probably disillusioned with the military after the election conspiracy that his colleagues perpetrated and Adama covered up. Good time for Gaius to swoop in and take advantage.

Very true. He did seem to be a real believer in the military and the system. He's a lot like Lee that way, and just as the assassination plan on Cain threw Lee into a tailspin, so the election fraud did the same for Gaeta. You could almost write a fic showing that parallel scene for scene. I could see Felix being easy pickings for a grateful and opportunistic Baltar. Baltar really had no one else he could trust and Felix was so naive.