Well I guess I'm the first to discover this, so I'm going to try my hand at making a 'how to' on it. Here goes.
It's pretty common to see people having issues with their power window motors, but now I know why. There is a resistor built into the motor unit, in series with the motor istelf. This is a temperature dependent resistor, where the temperature is determined by the current flowing through it. As the temperature increases, the resistance increases, allowing less current to flow. The problem is, these seem to get more sensitive as they age, resulting in the quite common "Motor stops working and I have to wait to use it again" issue.
All you have to do is bypass the resistor.
First of all, you'll need to get the motor out of the door. Follow your standard trim panel removal procedure (I use a crowbar) to get the trim off, and use a metal drill bit to drill out the rivets holding the motor in. You'll want to put some duct tape running up one side of the window, over the door frame, and down the other. This will keep the window from falling into the door when you take the motor out.
When you have the motor out, you'll need to crack it open. There are three metal tabs that hold on the plastic end cap, I found that a pair of large channel locks worked quite well for bending these.
Then carefully pry off the end cap. The whole thing will most likely be covered in a very sticky grease (marine grease?) that will give you some trouble in getting the cap off. Be aware that the motors brushes are attached to this cap and are under spring tension, so be patient and take your time if you don't want them to fly in all directions when you finally get it off.
Once you've finally removed it, the underside should look something like this:
That copper bar there with the numbers on it is the culprit. All you gotta do is put a dab of solder where the top bar is exposed to the bottom bar:
And just like that, it's fixed. But now comes the hard part: getting the motor back together. Initially I had tried to stick the stator back into the end cap with the brushes, and then stick all that back into the housing. I quickly found out though that the magnets on this thing are quite strong, and will just yank the stator straight out of the brushes. I did find an easier way though. Start by bending all the rear tabs on the brush mounts all the way out. Initially they should look kinda like this:
And you want them to look like this:
Now, you want to pull the stator out only enough to attach the brushes and end cap. But again you'll find that the magnets just want to yank the stator back down. What I did was I took a couple of flat iron bars (from a scrapped transformer) and stuck them down the sides of the housing, where there are gaps between the magnets. This was enough to hold the stator up, and I was able to remove them without disturbing the endcap.
Now you'll need to put the brushes back in. With the stator still pushed up and the end cap sitting on top, push the brushes through the backs of the brush holders. The brushes have a 45 degree cut on two sides, these sides need to go against the plastic end cap. Now put the springs in, and take a pair of pliers and start squeezing the end tabs together, just enough to put some tension on the spring. Push the spring towards the stator to make sure it is in all the way, and finish bending the end tabs back to their original position.
Remove whatever you used to hold the stator up (being careful not to dislodge the endcap), and push the end cap back down to its original place. Then bend the metal tabs back, and you're done!
It should be noted that this resistor was most likely a safety feature, cutting power to the motor when it was unable to move. This fix is done at your own risk.