I agree that fuel starvation is one of the possibilities. On my '99 Neon, and according to posts in another Neon Forum, it is NOT uncommon for the Neon fuel pump to fail slowly, only providing partial fuel pressure.
The adaptive engine control would adapt to low fuel pressure by increasing the pulse width of the injectors to result in the same volume of fuel being injected and thus the same amount of engine power. It can do this right up to the point the injectors hit their maximum pulse width, and if the fuel pressure is low enough, then less fuel than is needed will be squirted out of those injectors. Say like, flooring the accelerator going up hill?
The Neon (at least the later years) has a fuel pressure tap right on the rail over the injectors. Easy to put a fuel pressure gauge on it, mine showed pressure surging massively +/- 20 PSI from the spec 55PSI fuel pressure. I lived with it, then I started to loss power under high power/load conditions, then it got harder to start, then one day the engine took forever to start and when it caught it barely ran and flooring the accelerator just resulted in rpm barely going over idle and NOT having the power to move. I changed the fuel pump, and it does take a while to fill the reservoir in the pump, so it didn't start right away, it even died when I floored it on the test drive before it had a chance to fill the reservoir completely. But after a few minutes of driving it ran great, checked the fuel pressure and it held a perfect steady 55PSI, no surges, even when revving the motor a bit.