Does it do this every time?? Does it spit and sputter or just ease out kind of like idling down and finally die? How long until a restart is possible? Really sounds fuel starved. Do like cray said and take the bowl off. There is a rod and a needle inside the bowl on top of the float. Works just like the float in your toilet. The needle either has a rubber tip or there is an oring inside the inlet. Take the float off and pump your bulb. Allow fuel to flow through the inlet. I said something about the oring because if it has an oring inside the inlet and you pump the bulb it will blow it out and you'll lose it....don't ask how I know...lol. After you flush it put it back on and try it. You could have a piece of trash on in that inlet next to the needle. It has fuel when it sits but doesn't have enough flow to keep bowl full as you are running.
Its been a while and I do not remember if and where the fuel pump is. It will be a little square deal I believe it the model has one. It normally has a screen in it. The fuel lines will go in and out of this. There is a flathead screw in the center of it I think...or something similar. Take this off and make sure the screen is clean. Some also have a small inline filter on them...replace this.
Something else...while the bowl is off, take some compressed air....maybe 40 or so psi....not the 120 after the compressor shuts off, that will make a mess...lol. Blow air backwards through the fuel lines to the tank...slowly. That may dislodge something if by chance its in the line itself. Just some things to try...keep us updated.
"But if serving the Lord seems undesirable to you, then choose for yourselves this day whom you will serve, whether the gods your ancestors served beyond the Euphrates, or the gods of the Amorites, in whose land you are living. But as for me and my household, we will serve the Lord.” Joshua 25:15