Check for fuel spark and compression, one of those has to be missing. it could easily be a bad valve.
Cap and rotor plugs and wires may be worn
You have bad spark plugs and or cap and rotor
Sounds to me like you need to replace the spark plugs, spark plug wires and rotor. If the condition still persists, replace the distributor cap.
The gap on the plugs might not be gapped properly.
The RX8 has 4 spark plugs or two plugs per rotor. Each rotor has a leading and a trailing plug, the trailing fires a little bit after the leading plug.
start with dist cap and rotor
check your timing
Replace plugs, wires, cap, rotor, belt as needed. Also check all fluids.Replace plugs, wires, cap, rotor, belt as needed. Also check all fluids.
Bad ignition coil?
Disc brake rotor? A pulsation in the brake pedal when applied. Distributor ignition rotor? The engine may not run or run poorly with misfires.
This website should help. Good Luck! http://www.aa1car.com/library/misfire.htm
Very possible.