OP, I've had this same issue a couple times. Stumbled at about 500rpms and would finally cut out after about 10 secs. One time, it was stumbling and I turned on the AC fan, cut out instantly. After all stalls had a flashing battery light on the dash. It went through these stumbles for a couple days, like you said after startups after she had been sitting. Haven't had the issue in about a week though. Last time it started stumbling, I revved the engine and it went back to a normal idle.
Just providing my experience if it helps any. Was thinking a possible battery issue since I leave my iPod plugged in all the time and it never turns off...Still leave it plugged in though and no issues again so idk. :/