Does it run and drive all right some of the time? Or is it always doing the run for a few seconds and stop thing now? Does it get regular maintenance and filter changes? Sometimes it just needs a fuel filter. If it's a fuel injected newer Accord it may do that if the filter is clogged. Some fuel gets pushed through by the electric pump but the motor uses it faster than the pump can push it through the filter. So when you re-start it the pump has enough time to re prime (pressurize) the system it and will work for a few seconds again.
It could also be the electric fuel pump. If the car is older it could be wearing out and not flowing enough fuel to keep up.
That's just a few ideas. Of course a wise mechanic once told me that 90% of the problems we think are fuel related end up being electrical :) That's why the year of the car is important since the electrical stuff should last a long time before it gives you trouble. But sometimes computers go insane, 2001s HAL comes to mind :)
Aaron