My thought was the gas tank or gas cap wasn't venting or taking in air as gas was being used, causing a restriction in flow.
Next time you get it running,
let it idle 2 - 3 minutes,
turn it off
remove the gas cap
Listen for abnormal amount air being sucked into the tank &
see if there is an abnormal amount of fumes rushing out.
Use caution so as not to get gas sprayed on you in the event it should do so.
My thought on this--
If the venting is not working, the air can not replace gas being used, causing a loss of suction pressure. Similar to drinking from a plastic bottle-- the drink will stop flowing.
Im sure someone can explain it much better, & even tell me Im out in left field...LOL!!