Had a similar problem with an older Cub RZT50 that belongs to my church. Replaced all the fuel lines, the fuel filter, the fuel pump, went through the carb, and so on, and it didn't change a thing. Finally pulled off the fender that covers the fuel tank and discovered a brass 90 degree elbow fitting that fits in a rubber grommet on top of the fuel tank. The fuel line feeds from one side of that elbow, but the other side was fitted with a pickup tube made of rigid black plastic, like a big heavy drinking straw. There was no filter on that pickup tube, and the problem lay there. Something -- grass clippings, dead bugs, whatever -- was getting sucked up through that pickup tube from the bottom of the tank, and whatever it was was too large to fit through the brass elbow. The passage through that elbow is MUCH smaller than either the pickup tube or the fuel lines. The elbow was essentially a bottleneck.
The mower would stop at random times, but always start back up after sitting for a few minutes. Whatever was blocking that elbow would drift back down the pickup tube once the engine stopped, and it would be slurped up again sometime later. Lather, rinse, repeat.
What I did to fix things was remove that rigid plastic pickup tube and replace it with a length of standard 1/4" black rubber fuel line. I weighted the bottom end of it with a couple of steel nuts and installed a filter to keep out the inevitable tank-bottom crud.
That was four years ago. That old RZT is still cutting our grass, and it never misses a beat.
Also, FWIW, this fuel pickup design is very much a standard feature on MTD products. I have run into the same problem on other MTD mowers and I've been able to solve the problem in much the same way each time.
