Each copper line across the grid is a path for electrical current to flow from one side of the window to the other. As the current flows through the copper line, it generates some heat which drives off the frost or fog. If a copper line is even scratched, the path for the current is broken. No current, no heat on that section. The unbroken sections can still work.

I've done the repair and it does work. The copper paint that is used must make good contact with the old paint on the window. I used some very fine steel wool to carefully clean the old copper first, then I painted on the repair paint. Even then I had a "hot spot" at the repair showing that little spot had higher resistance. It's also hard to find the break in the old copper. Sometimes there are more than one break. I located mine using a multimeter on the ohms range then put a small piece of tape near the break to show where it is. After finding all the breaks, I did the repair. Maybe you missed a break. As for why it works only in the middle, I don't have an answer. I agree with you that it should work evenly unless the grid lines have come loose from the glass somehow. Have you measured the voltage at each side of the grid? I just went out and measured and got 10.0v in my 245 and 11.1 in my 244. This is measured where the wires connect to the grid.

I hope I haven't been telling you what you already know. Those defroster grids can be a pain to fix.