potkettleblack,
No, the MCC doesnt expire. Its a one off certificate which is required for Type rating purposes. Moons ago, airlines used to pay for the MCC, but now of course Pilots have to stump that one up themselves.
The only things that expire after gaining an fATPL are the various ratings - SEP, MEP, and MEIR. Not too much of an issue if the SEP or the MEP lapse but the MEIR must be current for a Type rating course. Best bet however is to keep everything current and keep flying.