I'll tell you everything I know:
I have had a weird fuel delivery problem lately where when a heavy passenger rides along, my miata will lose most engine power and I struggle to keep the engine running. It also runs a very rich idle when this occurs. This morning I couldn't start the miata after a five-hour interstate drive yesterday night. I believe it to be a fuel delivery problem, but I'm running out of things to check. I've replaced the fuel filter and verified my fuel pump works by applying 12 volts to it. One thing I just noticed while trying to start the car was I could feel the fuel pump clicking repeatedly (as if it were cutting on and off).
Any guesses or help are appreciated.

 

Read this. Step 4(a) deals with the most common problem I run into.
No-Start Troubleshooting Guide - MX-5 Miata Forum