I've got the same PZ P-51 and it's there little 1300mah 12c battery thats the problem mate,i've used two of them in my P-51 and they both gave up the ghost really fast and did what you said yours did.
So i went over to the Turnigy 1800mah 20c battery and i get more flight time and a faster P-51 now,if you want to try one go over to Hobbyking.com,if not just get a better make of battery than what PZ gave us with this plane,don't get me wrong i'm not knocking HH/PZ because i have loads of there planes and most of the PZ warbirds but i just won't buy the BnF planes now because of there batteries,i now just get there PnP ones and put my own Turnigy batts in there with my own RX.
I just tried to reply to this thread and my post didn't show up for some reason so if you see two of my posts saying the same sort of thing you will know why.