I have that problem, only i am using 2500ma rechargeables. I thought it might be the batteries so i bought new ones. No luck, still didn't work. Tried my batteries on my friends's gp2x, worked for 3+ hours. On mine they don't last 3 minutes.
I tried brushing the contacts. No luck. The batteries fit fine, they are not loose.
The console used to work fine, then I stoped using it for a few months and when I tried it again I had this problem.
It's really hard to find a solution and all my google foo won't help because so many people use crap batteries including the original batteries and most posts regard that situation. It's not my case.
Please help!!!