Just for everyone's info, I had the same problem with my 60C after about 6 months of use. The Canadian repair dealer returned the GPS to Garmin for repairs.
They replaced the "rear case" (and the scratched screen) under warrenty. Unfortunately, I sent it in on Dec 6, 2004 and got it back on Jan 6, 2005 but I guess the Christmas hollidays caused the delay.
I'm not sure if it turned off again today or not..... got my fingers crossed...
-Dale-