I have the same issues with mine(bought in July)...When I first plugin the light turns on and sometimes turns right off. Other times it stays on for a while(few minutes up to a few hours). I keep meaning to go to the Apple Store, but haven't quite made it yet.
It seems like when I first got it it didn't have this problem, but i first noticed the change at the end of August
Well you gotta love Applecare!!! I called on thursday and explained what is happening with my magsafe adapter. They sent out a replacement which I recieved the next morning.