Well, there's dead, and then there's dead.
The motor is a brush type that is fairly well geared down. So, it spins many times per inch of travel.
If it had a bad spot on the winding, brush, or commutator, It would hit it way before half way.
If the motor is truely dieing electrically half way down, then there must be a wiring problem that the window is hitting and knocking a wire loose.
What is more likely is the motor is stalling.
The leverage changes as the window goes farther up and down.
Apparently there is more load on the motor when it gets low.
A bad motor can and often does cause that, bad bearings, worn brushes, bad solder joints.
But, it can just as easily be caused by the mechanism binding, or low power.
First thing, if you happen to have an ammeter on the dash, turn the key on and run the motor down past the bad spot, and watch the ammeter when you try to run it up.
If its stuck, you will see a load that comes and goes with the switch.
If you don't, turn the key on, make sure the door is open, and watch the dome light.
If the motor is trying to work, it should dim and brighten as you work the switch.
If so, I would pull the door panel and check for binding, worn pivot points, or a bad gear track.
You could also consider the voltage boost mod. It involves adding relays in the door with heavy wire run to them from the battery or another strong power source so that the power for the windows does not have to go through lots of small wire and worn switches.