That's 'idle-droop'. Lot's of new Mazdas have it. No one knows why it happens, trust me on this. Find the idle set screw (8mm locking bolt w/small allen screw in Miata) on throttle assembly. Turn allen screw one-half turn clockwise; lock nut. If it idle-droops again; turn another half-turn clock (keep 9mm & allen wrench handy). Repeat until idle-droop ceases. When idling revs begin to climb above 11-1200rpm; turn idle screw one-half turn counterclock. Repeat until idling revs behave. Turn back clock when idle droop returns. Repeat. Repeat. Repeat.
Steve McMahon Green JRSC '00LS