First thought it sounds like a clogged fuel filter/filters, but you said you've change them already. Second thought is something in the tank finding it's way down to the fuel suction tube and blocking/clogging it up wht in operation. What happens is vacuum from the fuel pump will keep the item sucked against the line when in operation but when the machine stops and vacuum goes away it eventually floats off until the next time. Next thought is a small crack in the fuel line somewhere letting the system suck in a bit of air as the machine is running. Once it shuts down the fuel flowing trough the system before it starts again displaces the air and it runs fine again until it sucks in enough air to cause a problem.
Over the years I have seen all three things happen, and, unfortunately except for changing the filters figuring out what's really wrong can be a royal PITA. Even then you still might not know what exactly was wrong unless you physically find the item blocking the intake or a visible crack/hole in the line... In fact there is one Hitachi excavator out there I was called on where the problem finally got resolved after about 4 different trips out and every check I could think of to make turning up absolutely nothing wrong, by replacing what appeared to be a perfectly good factory fuel line. I disected the old line from one ond to the other and between me and the customer, we have yet to find a crack hole, or anything else visible....but the machine is running like it should be now.