I suspect you'll probably end up having to replace the timer, but you could try cleaning it. I would imagine there's a fair chance it may be gummed up with oils, carbon and all kinds of other volatiles from cooking.
Get yourself a can of electrical parts cleaner and spray the heck out of the timer. The cleaner will evaporate completely so there won't be an residue left in it when you hook it back up and try it. If there are any openings in the timer, use the red tube to direct the spray inside to wash it out.
Outside of disassembling the switch, which may or may not be possible, that would be my best suggestion.
Hope it helps; let us know how it goes!