I would try the RX8 forum since it has a rotory engine. I know there was a bunch of issues with the 8's motor and Mazda even had to replace alot of them.
The problem is most likely your apex seals. It is a common problem with the RX8. I owned one for just over year and had the same issue. After everything gets hot and expands, the seals are no longer as effective and make it difficult for the engine to create enough compression to start. Rotary engines are ALL ABOUT compression. No compression or low compression means no fire.
BUT IT STARTS WITH A PUSH START VERY EASY
Looking for a Used RX-8 in your area?
CarGurus has 432 nationwide RX-8 listings starting at $2,995.
Search Mazda RX-8 Questions
Are you a UK consumer? CarGurus now has a discussion forum in the UK.
Mazda RX-8 Experts