Rotaries aren't the most reliable engines. They're massive fun and they're smooth as silk, but because it's so smooth, you tend to not notice when you're over-revving. But even if you treat it well, the fact that you have a rotor scraping the inside of your engine means it MUST cause damage. The exhaust gases are also pretty hot for a non-turbo car and that could cause detonation.
Rotary engines burn oil. That's just the way it is. Check your levels every two to three weeks. I would definitely put in a type of oil that would provide lubrication at high RPM. Also, synthetics are very bad because a rotary engine, just like a 2-stroke engine actually burns off oil and synthetics resist being burned off. Some folks actually mix their oil with 2-stroke oil. Ask a specialist rotary performance shop about this.
Second, when they are revved to high RPMs the apex seals may damage the inside of the engine after a while. This damage is referred to as chatter marks. This is caused by carbon build-up (see the next point). To minimize this damage, you need to use an oil that will lubricate your engine sufficiently when revving as high as a rotary does.
Third, it is very important to rev the car to its limit at least once a week to burn off excess carbon build-up. Or just go for a nice, spirited drive. Allow the car to warm up properly beforehand and cool down after. This is also a good idea for turbo owners. I don't know if it's as important in the RX8 as it was with the RX2 and RX7, but rather safe than sorry.
And finally, keep in mind that the rotary engine is a high-performance engine. It isn't intended to be used at slow speeds, crawling through traffic. Overheating a Rotary is VERY bad.