To start off, I've had similar issues before and fixed them. Now, after having my RX-7 for about a year, I've started having a new issue after I had her running very well for a few months.
There are no vacuum leaks that I have found, the compression is also in good working order. It has been tuned by professionals as well.

Basically. If I let it sit at idle, and am not giving it gas, such as at a light or coasting down a hill, it will try to die. If it dies, the engine floods more often than not and I have to WOT and crank for a few seconds or more just to start it. Sometimes it can do this every 10 minutes while driving, or it won't do it for a few hours, but it usually does it daily. Starts up great otherwise. Drives great as long as I'm not sitting at idle. Videos below show what it's like as it starts to die vs what it's like normally while driving.

Dying

Good

Both of these videos were taken within 30 minutes. The dying video was about 10 minutes after starting the car while letting it warm up after 4 hours of sitting, the good was taken about 20 minutes after the dying video once I got home.
I have been looking up other threads from things that can cause this, and I saw one of them could be the coolant seals. My coolant has not gone down in over a month, Sitting about an inch under the cap in the same place that it always is. I haven't changed the spark plugs in a while but I'm not sure if that's the issue, will do that this weekend. Another said it could be grounding to ECU, but I've never seen anyone else ground their PFC and I don't know if there's a certain place it should be grounded to or if the chassis is fine. Could really use some advice here. Not sure if it's a fuel issue since it runs perfect as long as it's not at idle at the wrong time. Thanks in advance!

 

Couple of questions when the engine floods does this happen on its own or did you try and give the car gas while coasting with the engine off? btw a coolant leak wouldn't cause the issue.

At first thought this sounds like one of two things. A timing issue or a vacuum leak. I would check the turbo inlets to ensure they aren't leaking and then you'll have to tackle the rats nest. Since the rats nest is a challenge I attached a diagram which might be helpful.

 

I don't believe it's a vacuum leak. I'm starting to notice that it's not "dying" at idle, it's completely flooding at idle. It floods while at idle, and if I floor the gas to stop it, sometimes it will stop it from dying, other times it will just flood over and die. I assume it's an injector or fuel issue.