When it starts back up, does it restart easily, need a bit more "crank time", and/or does it smell of gasoline and restart with a cloud of black smoke from the exhaust pipe? When this happens, to confirm, which end of the vehicle is higher than the other one? What fuel level is in the fuel tank? Are these easy stops or otherwise? From what speed?
As the jsts in the BBD are more toward the center of the carb, it would be hard for a "nose-down" attitude to uncover them. As the BBDS are not very prone for the air horn to warp upward from over-torque of the air cleaner wing nut (as the Stromberg WWC and Hollley 2210/2245 2bbls are), I feel safe we can presume the gasket between the carb body and air horn (where the rear of the float bowl seals, separatring it from the venturi area) is working as it should.
Any vacuum leaks when the brake booster is activated? Hissing? Engine missing or running unsteadily?
Oil level in the engine? Which might trigger a low oil pressure light as a result BEFORE the engine stops?e
Any possisble wiring harness interferences with the brake pedal mechanism, under the dash?
That's about all I can think of.
Take caree,
CBODY67