You can limit it to three possibilities:
#1 (and the most likely) - Fuel Starvation
When you turn the gas on and start it up, the carb's bowl is filled with gas. When it is running, that gas in the bowl is burned up but there is something stopping the fuel from coming in fast enough to keep the bowl filled causing it to die. When you let it set for a few minutes, the fuel flow has time to catch up and fill the bowl back up. Re-check the petcock, petcock filter, fuel lines, and the bottom of the tank where the lines plug in to (you can take a piece of wire and run it through the openings) If all are clean, check the gas tank cap. If you have to, drill a very small hole in the cap for ventalation.
#2 Bad stator coil
On some bad coils, the machine gets great spark until it warms up and then the coil goes out until the engine has time to cool down. Fire it up and as soon as it dies, pull the plug and check for spark. If you don't have any, you will probably have to replace the primary coil. (Check #3 first)
#3 Kill switch wires grounding to the frame
This happened to me on my 110 and left me clueless for days. I cleaned the carb, bought a new stator, checked the timing, and so on. Well I would start it up it would run fine for about 5-10 min. and then die. I would let it set and it would start right up. Thats why I thought it was either a #1 or #2 problem. What happed was, even though it was a very very strange coincedence, when I started it the kill switch wires were off the frame letting it start and run but after a while the wires vibrated so much that they found their way to the frame, which grounded them out.
Good luck and let us know what you find out!!
Justin ~hondaATCman~
'82 Honda ATC 110
'81 Honda ATC 250r (Summer Project)
'87 Suzuki LT 250r Quadracer - Very Modded...FAST!!
'03 Yamaha Big Bear 400 4x4
'85 Ford Bronco II 4x4 2.8 V6