I have a 2001 Miata with 60K miles, and I have been plagued with the start /stall problem for the last 5 months. Mine exhibits  no security light when it will not start. If I try more than three times in a row, it goes into lock down mode for a long time.
 I had three new keys made, Replaced the EGI relay, checked all connections and it worked for about 10 days and the same problem reappeared. I also tried a “bad” key and the immobilizer light came on but car stalled.
 Two dealers could not find the problem.
 Any suggestions?
 Thanks