I checked my Haynes Repair manual and it states the following information:
Engine Isssue #6 Engine Starts but Stops Immediately:
1. Loose or faulty electrical connections at distributor, coil or alternator.
2. Insufficient fuel reaaching the fuel injectors.
3. Vacuum leak at the gasket between the intake manifold and throttle body.

I could not find a listing for the exact problem that you are having. It's my
guess that #1 is the most likely cause of your problem. In addition, there
may be a "short" in the electrical wiring running to or from the
distributor, coil or alternator. Shorts are hard to locate since they can
only be found when the wire is shorted out at the time of the test. I
should also note that the distributor, coil or alternator may be
defective.
Jason

Only a partial response here....

Having to turn the key off and back on suggests the ECU is deciding the
engine isn't running and shuts off the fuel pump as a safety measure
(standard in modern cars). It may be deciding that because the engine dies.
Another possibility is that the engine is dying of fuel starvation and with
pressure bled from the fuel rail it won't figure out the right mixture in
time. One more: the ignition switch may be failing and only moving it all
the way back to off will patch it up again.

The crucial question is whether the engine is dying because of fuel or
ignition problems. The driver gets two good clues: if the tach drops like a
stone and the power disappears like you flipped a switch the ignition is
going away. If the tach follows the engine speed as it fades, and the power
seems to sag to nothing instead of lurching, you have fuel delivery
problems.

One final thing: if it acts like ignition and the warning lights don't come
on until you turn the switch off and back on, you can bet it's a bad switch.
(Outside chance it's a cracked connection inside the battery, but the switch
is the way to bet.)

Start by reading over http://tegger.com/hondafaq/faq.html#startrun and see
if anything rings a bell. It is a very good bet the problem is one of those
mentioned; actual fuel pump failures are rare in Hondas, for example. Since
the coil has been replaced twice we can pretty much rule that out. That
leaves you with three classic trouble areas: the Main Relay (fuel pump
relay), the ignitor and the ignition switch. As the driver you probably have
enough clues now to decide on a course of action. Good luck!

Mike

It could be so many things, but next time it happens note if the idiot
lights on your dash come on. If they do not come on when it stalls, I'd
check the ignition switch.

Remco

If the coil is truly good, then you have an igniter problem.

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Could be somebody forgot to replace the heat-sink compound (just like on
a Pentium processor) on the backside of the ignitor and it's overheating
now that the weather is warmer.

'Curly'