You need to isolate the problem. You do have enough fuel in the rig, correct?
It take 3 things for it to run
Compression
Fuel
Ignition
You basically have compression or it wouldn't run at all. You have ignition but you could be losing it. You have some fuel because it tries to run. When it dies out, you need to prove if it's the ignition or fuel. Use a spray bottle with a small amount of gasoline in it to spray the carb throat as it begins to die out.
If it recovers and tries to run then it is in fact not getting fuel. If it dies out anyway, it could be losing ignition. It could lose it's ignition for a number of reasons but a common one may be an issue with the low oil shut down or low oil pressure.
Have a fire extinguisher on hand and a garden hose. I do not know your capabilities but people burn their houses and garages down doing this stuff. Be careful. Just trying to be sure you dont have a disaster.
If it recovers when sprayed with gas you then need to prove why it's not getting steady fuel. It could be a bad fuel line sucking air at times. A restricted filter. Plugged pick up tube.
I know the pump is new but...The pump has to be able to produce pressure but also deliver volume. If its an electric pump and you were to pump fuel into a bottle you would see that it should spurt out at a pretty decent rate and fill a pop bottle in seconds not minutes. If it is erratic look for air leaks in the line. An air leak in the fuel hose can be an aggravating problem that only shows itself at times.
The proper way to address the carb is to remove any jets and thoroughly blow it out with compressed air. The problem is that some carbs and jets can be a real pain. If the bowl was not full of crud or varnish you may not even have a carb problem. if it was trashy in the bowl, sometimes the carb cant be saved. The best carb soaks are with a product called hydro seal made by gunk. It's nasty stinky stuff that I would only use as a last try. It will eat ALL rubber parts so you need to be careful with it.