It would help to know what year and model this is...

Next time the problem resurfaces, listen carefully as you turn the key
from Off to Acc to Run. As you get to Run (not start) you should hear a
relay clicking (turning on the fuel pump) and then around 3 seconds
later you should hear it clicking again (turning off the fuel pump). If
you do not hear this, it could be a broken main relay (fuel pump relay)

Keep in mind that depending on your year and model, this information
might be completely irrelevant.

If this is a Honda, my first bet would be on the ignition
coil.

Year and model, please?

Also, status of routine maintenance, like spark plug wires,
plugs, etc.?

See also http://www.tegger.com/hondafaq/faq.html#startrun 
for typical other causes of Honda run-start problems.

drewer <none@000.com> wrote in news:982341_abf1f3c351cf38a4f329e91005e65e79
@autoboardz.com:

Ignition switch or igniter. Most likely igniter at this point.

If you have a tachometer, does the tach needle drop suddenly before the car
stalls? When you crank during the no-start episode, is the tach needle
dead still, or does it jiggle a tiny bit?

Do you mean the "Maintenance Required light, or the Check Engine light?

If the Check Engine light, you need to get the code read that's behind the
light. For that we need to know your year and model.

And you bought the car anyway? Not a good idea.

When you bought the car, did it come with a year, make and model?

Like I said to the last poster who also indicates that his/her service
indicator is on, why make guesses as to what it is when the car might be
trying to tell you.

Your symtoms could be a common thing, or not, but the code will tell.

Why would to buy a car with the Service or check engine light on without
finding out way?  This amazes me.

If it is a "Check Engine" light, take it to AutoZone or a place like that
and if the car is newer than a 1996, they can hook up the OBD II code
scanner and tell you why.

G-Man