You may not be getting enough juice to the motor - have your battery and alternator checked. The engine should run off the alternator once started but there's still a trickle when you let off the engine, like at idle when the voltage drops - at that point it's relying more on the stored energy of the battery - if you have a bad cell it can cause the engine to power down and you end up losing it at the plugs - when accelerating you have more available amps at the alternator so you don't see the power loss. Have you had any issues starting? Just some suggestions.

-- John