Engine starts then dies

Pintsize725

This has happened a few times over the course of the last year or so. There are no warning signs that I've noticed. It's happened after leaving the car off for only 20 minutes and also having it off the entire weekend. The gas level always varies. Today I had 3/4 of a tank and it happened after sitting for about an hour and 20ish minutes.

I'll press the brake, hit the start button, release the brake and let the engine start. The engine will start and then immediately die. I can't get a video of it because I never know when it will happen. Sometimes it takes about 5 tries to get it going but I never remember to bust out the camera during those times. When the car finally does start, it stutters like it's about to die again and then just idles really low before stabilizing. What do I need to check since I can't really replicate it on command?

This video was taken after about two times of it not starting:


This was today, after one time of it shutting off. It started, almost died and then just stabilized:


I'm wondering if maybe my fuel line(s?) near the exhaust are compromised. I didn't use the guard provided by FI since I didn't buy it new so the lines were wrapped in a fire sleeve provided by the shop.

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Tracie