Is there any noises coming from the dash, like a "bing bing bing" when it cuts out?
If so when you are driving, try turning off the engine and back on again, if this then makes the accelator work it COULD be your "TPS". (Throtttle position sensor) your accelorator has a little computer in it, not a cable and this could be your problem.
It was for me and it sounds like the same problem.
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