What would be the problem with cruise control shutting off on 2005 mit. lancer?
There is no one specific fuse according to the Lancer manual that relates to only cruise control (according to my 2008 Lancer owner's manual, anyway). It might be tied-in with another circuit related to it. The best thing to do would be to check continuity for all fuses in both fuse boxes (in the engine compartment and under the steering wheel), and any blown fuses might be your issue.
Another possibility could be the stop switch located at the top of your brake pedal (you'll have to remove the panel under the steering wheel to get to it). If this switch has failed, the engine's ECU won't recognize the stop command electronically. While the car will still stop, this electrical signal is necessary for cruise control to be active. The biggest give-away is that typically when this switch gives out, your brake lights won't work either.