I have had the same problem with my MBP Core 2 Duo. Looking at the MagSafe plug on the power adaptor, I noticed some of the pins were shorter than they should be. That, and it looked like there might be scorch marks.

I think my infant slobbered on the MagSafe plug without me realizing, so it was wet when I plugged it in. Since I have replaced my power brick a month ago I don't recall having a shutdown problem.

My other thought is shutdowns could happen if the battery gets bumped loose. I believe that happened once and I found the battery latches became dislodged.