Starts and runs so that would eliminate electrical issues, doubt that running for a minute would heat up enough to cause "thermal failure" of mag, etc. Definitely sounds fuel related. take off gas cap and see if it starts and runs normal, if it does, plugged vent in the gas cap. Could be an intermittent electricl connection though, when it starts, things could be rattling around, making and breaking contact, inspect and rattle all wireing. I'd pull the carb and give it a good cleaning, get a rebuild kit, depending on age of the unit. Pay special attention to fine orifices in there, "ream" them out. "ties" in produce section of market, paper over fine wire, remove paper and use wire as a reamer. Will it only run when choked? if so, another indication of carb issue.

When it's running again, make sure you add stabil or equivalent to the gas to offset the ethanol in gas we have to buy today. Also, SeaFoam added regularly, in addition to fuel stabilzer, does a great job of keeping fuel circuits clean and happy.

Good luck,

Ev