My 1998 Mazda ESV6 Automatic has an intermittent start problem at 100,000 miles. The car will start and run very well some times. Other times the engine will crank and not start. One can return to the car ihe next day and the car will start easily on the first crank or two, or not at all. The spark has been tested during no start cranking and found good on all three cylinders of the front bank.
Also the car will not start sometimes after a short drive of five miles or less, when the driver returns a couple of hours later. The battery is recent and well charged and the cranking is powerful and continuous.
The dealer replaced the fuel pump and relay and the battery ground cable to no avail, and claimed they were unable to pull a trouble code because the car always started for them.
The dealer also suspected the ignition key chip and the ignition lock, but after successfully trying the unused spare key decided this was not the problem.
Can you help????

 

I don't believe your dealer. What some stupid (or lazy) mechanics will do is deliberately or accidentally clear all codes prior to running the OBD code reader, thus wiping out all prior history! Get on their backs and insist on a hard copy print out too. There is no way that you can have the sort of problem you describe without a history in latched memory.
The other possibility is that they disconnected the battery prior to doing the OBD readout, in which case of course, the fault codes would be wiped out.
I don't know the Mazda 6 cylinder, but on the four banger, I would be looking at the pressure on the fuel rail; a defective fuel pressure regulator can do what you describe, but so too can a problem with the evap purge cycle on startup.
Maybe a visit to a recommended dealer in your area might be in order.