AI Eyes are a direct feed back to the AI core network: when player ships gang up on the AI overwhelmingly, alarms are tripped and higher-level AI ships come pouring out of the Eye. Either kill the eye first, before bringing in your gigantic fleet, or just do guerrilla-style raids on planets with an Eye. Specifically, the AI Eyes make sure that your ships only ever outnumber the AI ships 2:1.
Does that answer it, or something more specific?