What position was the shifter in when the car did start? Also, does the shift lever feel loose/sloppy?

The reason I ask is the neutral safety switch will allow a start in either the "P" or "N" position. It is common for the the switch contacts associated with the "P" position to fail. Failures usually start as intermittant and progressively get worse. If the shifter feels loose/sloppy you probably have a worn out/missing shift mechanism bushing. This can result in the shift mechanism not positioning the neutral safety switch correctly. This will also prevent a start.

Next time you have a problem, try starting with the shifter in "N". (If memory serves me correctly, you will have to insert the ignition key and rotate it to the first click, then shift to "N" and then turn the key the rest of the way to complete the start)

If you can start with the shifter in "N", you have a faulty neutral safety switch.

Please post your results......................