how to fix the engine cutting out?

Our engine, once warm, has started to cut out unless we are applying full throttle; it then recovers in fits and starts after varying times and drops in speed, only to start cutting all over again as soon as the foot is lifted from the throttle, however slightly.
We have tried various remedies - garage diagnostic machines show no problem; we have removed and examined the fuel tank and not found water.... 3 garages have failed to find the fault. Can anyone help?
It's a fiat ducato van 2.0 litre petrol engine, 1998 R reg