If you have confidence in the ignition it's time to indeed consider fuel issues. Unfortunately, we can't easily watch fuel flow under the circumstances which surround this failure. It sounds like the fuel supply is not keeping up under driving conditions, even though it is more than adequate under static test conditions. So what's different? The fuel is being mildly agitated in the tank. The fuel pump needs to actuate at a much higher rate. Certainly the demand for fuel is higher than at idle. I wonder if the fuel pump is "sticking" at the higher rate of actuation. This is unusual, but I have seen it happen in the past. The other thought that occurs is that perhaps something in the tank is being sucked into the feed tube until the engine dies, whereupon the suction lessens and whatever was blocking the egress of fuel floats away. Also not that common, but it has indeed happened before.
I'm not convinced any of the above is what's going on here, but it's something to inspect. Some electronic ignition failures will also mimic this behavior, but they usually worsen quickly and stop refiring. How long has this been going on?
Motorbill
From Lola to Land Rover, If it's British and has wheels, it's likely I've bloodied me knuckles thereupon