I had a similar problem with my sons LT50 (2 stroke). bike would start, idle ok (not good), but would either not rev or die when you gave it gas. I had the throttle limited for my son and thought it was a fouled plug. replaced plug. same problem. clean air filter, changed gas/cleaned filter. I thought I had it fixed, but had the same problem. I had a tantrum and lifted the back of the bike up and free revved the engine. about 20 seconds later the engine came to life. put my son the bike and it worked fine. about once to twice a weekend I'll have to do this. I think the engine itself gets loaded since it isn't being revved out and burning the oil out. don't know. it was the fix to my problem.

 

my 2 stroke is happiest wide open, we'll putt around a while, but then we gotta blow the soot out of it. it is happiest wide open. my opinion, my experience.....

 

Update for everyone out there. I had same problem with my LTZ 50. Cleaned carb and fresh gas still the same. One thing that nobody has said they tried yet that completely fixed mine was the line that went to the carb bowl vent was clogged. There is also another vent line on the same side that goes to the crankcase located between the pull start and a ground. Use compressed air and clean both line and I promise ur problem will go away! I accept tips by money order or checks lol jk. I believe the problem on mine was the bowl vent being clogged and wouldnt let gas in the carb like it should. Hope this helps someone out there.