Stalling CR125...

Hello Everybody,
Been working on a friends' (1990) CR125. Bike has been sitting for about two years. Can't figure out something; bike usually starts with a kick or two, will run for about 30 seconds to a minute and then bwaaa bwaaa dies! While it runs it reacts perfectly to the throttle. I checked and replaced carb with a known good one. All jets and settings are at stock. Reeds are perfect also. When it stalls, the spark plug is wet with gas. Usually drying and reinstalling the spark plug will start up nicely but with same results. I also notice a small backfire occasionaly.
The one thing that I noticed is that the copper coil on the stator looks like it has overheated in the past (plastic isolation is cracking) and it is actually a little loose in the housing! is this normal or is a short circuit to blame? Any way to test the coil out of the bike? Thanks for reading and thanks for your feedback.

Thank helio lucas and whenfoxforks-ruled. I appreciate your help. I did replace the fuel line and the complete carb. I noticed a small fuel leak on the tap so while working on the bike I replaced the tank with my sons' CR80. That should eliminate any problem with fuel and carb. Because after replacing these, problem was exactly the same. I will be checking the coil and replace the spark plug just to be safe. Throughout several (short) runs I have not noticed a dropping coolant level so I'm pretty sure coolant is not getting into the chamber, but I will keep an eye on it. I will update if I find anything useful. I will also be looking at the archives for anything similar. I am familiar with Eric Gorr. But Blair and Rohrich are new to me. Thanks for the info guys!

Problem solved! I checked the stator specs and everything was ok. I'm still concerned about the loose coil, but that was not the problem. I do not have an air filter installed at the moment and the silencer is definitely in need of a repack, exhaust port was surprisingly clean. Carb was replaced with identical unit. So, none of these could be the culprit. I did not get around to the compression test but I had a bright idea last night. My best ideas come to me when I'm half asleep :-). Today I reinstalled the stator and replaced the spark plug with a known good one. That's it! The friggin' spark plug solved everything! I have never seen a plug do that, but I'm convinced that this solved the problem. How can a spark plug work for 30 seconds and then quit, over and over again? Has anyone seen that? The engine runs fine. I need to adjust carb but it revs up nicely and does so until I shut it off. Yahooo!! Thanks to all who took the time to help. It was a good lesson for me. Try the simple stuff first! Take care.