I would verify a few things:
1) Check to see that the fuel tank vent hose is clear. They can get plugged by insects that decide to build a nest in them.
2) Verify the anti-syphon valve at the top of the tank is clean. You need to remove the fuel hose and unscrew the anti-syphon valve from the tank fuel supply down-spout into the tank. It has a check on it that can get gunked up.
3) When it dies, look immediately at the carb and see if fuel is dripping down the throat of the carb (without touching throttle). If it is, the float is set too high, which probably isn't an issue if you haven't touched it. However, the float may have become saturated and is not shutting off the fuel flow. That would require a new float at very minimum. A carb rebuild may be in order.
Or, the needle/seat are dirty or shot which again, isn't allowing the fuel to shut off. Replacing and/or cleaning is the fix for that.
A third option is the fuel pump is putting out too much pressure which, one more time, is keeping the needle/seat open and not shutting off fuel flow. Again, probably not an issue if you haven't changed the fuel pump.
4) If the pump shot is non-existent, you may be due for a good carb cleaning and rebuild.
I find it hard to believe that the fuel pump doesn't deliver fuel and then majically start working again. You could rtake a small can of gas with you and temporarily disconnect the fuel line from from pump and run it from the gas can. This effectively eliminates the tank to see if that's where the problem is.
Keep us updated.