Had a 2004 Sunfire a few years ago that would just cut off while going down the road. Just like you shut the car off with the switch except the radio and all would stay on, I would just notice I was decelerating instead accelerating and the power steering wouldn't work. At first, you could pull over, put it in park and it always started back but the longer I let it ride the worse it got til it just didn't start at all. Long ass story short, it was the fuel pump.
Well maybe I went around and fed cows and checked on things on my way. But we can take the cake box off and the flat bead put the factory bead back on it and you would be good to go.
Talked to a mechanic buddy of mine just now and he said to check the fuel pump fuse/relay. It's a very common problem.
There's a fuse box under the hood and he said "Off the top of his head it's fuse #18". The fuses will be labeled on the underside of the fuse box cover that you remove. It's part relay and part fuse. Pop the fuse out and clean the contacts good. Make sure the pins make good contact when you put it back in. Might fix your problem for nothing.
I would think if the fuse popped the pump would have just quit instantly and instead of losing acceleration slowly the car would have just quit right on the spot.
If it is the fuel pump then when you turn the ignition it will literally just click. Without any gas it won't even attempt to start.