Hello! My name is James and I am the third owner of a 2005 Shinka Edition AT RX-8. After obtaining the car I noticed the intent on not starting after it was hot, and the various annoyances that these cars are known for. However, here recently something has been happening that's making me question exactly what's wrong with it.

I go out to start my car, drive it maybe a mile and a half to the store. Park it, turn it off, go inside and get my groceries, come back out, go to start it (of course it takes forever because it needs a new starter, ignition coil, and plugs, or at least as far is it taking forever to start that is my theory) once it's started if it goes below 1500 rpm it will die. If I put it into gear, it dies, unless I keep the rpms up and quick shift into reverse/drive, and then if I do that, if I come to a stop sign or get behind a slow car, it will die. It only does it if I start it, go somewhere, spend a few minutes, then try to go and leave again. If I leave it sitting for an hour+ it will start fine and stay running.

I don't think it's a loss of compression issue because there's no loss of power. I'm thinking it may be the fuel pump going out since I know there's an issue of them not wanting to start once they're hot, but I don't understand how the car would get so hot so quick if I'm not running it to edge of the redline and only driving a max of 3 minutes to the store and back. I was also thinking maybe it's just a problem with the plugs not sparking once it's warmed up, but I'm not an expert mechanic. The only thing I really know how to do is change a tire, brakes, and check all the fluids.

Any help would be great thanks!

 

Sounds like an engine with bad compression.
If it runs good with no CELs, or loss of power, then I think ignition issues aren't the main culprit.
Unless you habitually drive it under a 1/4 tank, I think the fuel pump overheating isn't either.
It doesn't take long for the housings to expand when you drive it, that's where the loss of compression & hard hot starts come from.
There are many other things you can try like cleaning the ESS & MAF sensor, & the 20 brake stomp, but I would suggest you get a rotary specific compression test.