Sounds like a fuel delivery issue to me.....
Is your car under warranty? If its out of warranty you could take it to my husband at Big O. He's a pro at diagnosing issues like this.....
This kind of stuff was a regular issue when we were into rotary motors... So much so that I began to get a knack for knowing the issue before a thorough diagnosis. Not that this has anything to do with a rotary.... Because I've gone back to pistons.
however I had a fuel delivery issue in my last mustang with similar symptoms.