Check for fuel spark and compression, one of those has to be missing. it could easily be a bad valve.
You have bad spark plugs and or cap and rotor
Cap and rotor plugs and wires may be worn
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
Replace plugs, wires, cap, rotor, belt as needed. Also check all fluids.Replace plugs, wires, cap, rotor, belt as needed. Also check all fluids.
check your timing
Bad ignition coil?
This website should help. Good Luck! http://www.aa1car.com/library/misfire.htm
Very possible.
check your distributor cap and rotor, check the coil, check the wires, check fuses for ignition.