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Does it run longer if you choke the carburator (turn on the choke)? It may just be cold if it does. Choke it and keep it running and slowly take the choke off. Carburated (I assume) engines use more gas and then need choke when the parts are cold. As they warm you need less gas for it to run and the choke can be slowly taken off.
If this is not he problem, check your fuel source ie, is it getting fuel? the pump working? try a gravity fed line attached to the carb intake?
email me @semerm12@dreamscape.com and I will help more.