Very few sports/hobbies allow titled players to lose thier titles (sumo is a good counter-example), so on this logic alone Id say no.
The reason you don't see GM at 1600 FIDE, is probably because once they have learnt to play chess at the GM level, its almost impossible for them to as crap as a 1600(without trying).
that or they would just retire to save themselves from utter embarrisment.
I was wondering if you could lose your CM/NM/IM/GM Title?
I doubt it you can.. but i really dont got a clue..
i have never seen a GM 1600 FIDE rated for example if he got to old and then he sucked.