Rear Axle dead on 87 stang

When I first bought my car both my tires would spin during a burn out or when I peal out, but now it has gotten to the point where only the passenger side wheel spins during a burn out and I leave only one 10 foot tire mark instead of 2. I have heard of this happening before when the rear axle dies but is there anyway to repair it or do I have to buy a new one for 500 bucks, Ive seen these rebuild kits on ebay saying they will fix a burnt out axle. Do those really work? Any help would be appriciated.
 
Well if its the stock ford diff. all you have to do is buy a clutch rebuild kit and replace the clutches in the carrier.. They always wear out specially when doing burn outs.. Thats when you upgrade to a detroit locker hehe. Wish I had the extra money at the time, when I bought my Eaton posi.. Its holding pretty good though I have to admit
 
Burn outs

Yeah I didnt think doing burn outs was good for any part of the car especially the diff. but hey burn outs kick ass lol, thanks for the tip, looks like I need to buy a rebuild kit for my diff and then buy a few more extra once I burn it out again. Ive gone through 2 sets of rear tires so far, everyone I show the car to wants me to do a burn out lol.