I had a similar prob with an automatic mazda.
Took ages to find, although mine was cutting out completly when i took foot of gas pedal,
Turned out to be water in fuel, causing engine to cut out,
If car had been manual the momentum of engine would have pulled it through,
I found it by putting an in line water trap in the fuel delivery pie,
The water was getting into the tank via vent pipe to fuel tank, just under rear wheel arch.
am I right,
I'm not wrong.