I know exactly what you mean, and for some reason, I doubt it's the timing belt, considering my car is an 05 SX 2.0 with only 12,000 kms on it.
I would recommend checking your igniton system. For some dumbass reason, on the Neons, they seem to have some ghosts. One of them is what you've described. I had that problem previously and it was pinned down to a misfire in the 4th cylinder, caused by a faulty spark plug. It was replaced, and the problem went away.
If you go that route however, just replace all four with aftermarket plugs. I know my baby is getting all four, plus wires, plus the coil pack(NGK Iridium plugs, which the Neons love, and an MSD coil pack, as well as MSD Superconductor 8.5mm wires)