sounds like its just off timing a lil bit, does it shut off while ur driving or when youre at a light???

 

if you ever get to where you cant do fix it or need used parts call jeff and mazdtech (813) 874-0937...worked for mazda for years and now has his own rotory specialist shop...the guys knows his shit and is a nice guy as long as you dont try to bs him and get on his bad side.

 

sounds like a bad coil, when they warm up the stop working until they cool off again, then they work.

when it dies on you just pull the plug wires off the coils and turn the key to try and start, you should hear and see the snapping of the coils sparking. if one is sparking and the other is not. It should be the leading one out, cuz the engine will run with only the leading working, but not run if only the trailing is working. so if this is the case swap coils around, to get you home or the parts store. The trailing plugs are mainly for emissions to clean up the left over un burnt gas. good luck!