Zoomie- This sounds like your engine has an air leak somewhere in the case, causing excess air to starve the engine of fuel so it stops running. Check the intake boot to cylinder, seal o-ring with permatex ultra grey, also the joint between the cylinder and crankcase could be loose and needs re-sealing, or the last spot is the crankshaft main bearings and seals (usually the seals are molded to the bearing so it's one piece actually), even though the bearing could be fine the seal may be faulty. Does it "four-stroke" at full throttle?
Also, check the fuel tank cap for a faulty vent valve, try running with the tank cap a little loose, if it runs good then the cap is bad. Your unit is fuel starving for one of these reasons.

Did you ever find the cause of your Husky shutting off? I have the exact same symptom