my speedfight 100 cuts out at low revs?

when i start it up it tiks over for about 45 seconds and conks out its a 2003 model and it had a full engine rebuild 2000 miles ago Ive checked spark plug ,air filter exhaust its OK if the revs are on (not enough to pull away)but as soon as the revs are let off it sounds fine for 30 seconds then after that it sounds like it wants to cutout and then eventually it does .i just want every thing to work perfectly please help me