While we can never be sure of the cause of the mechanism freezing up, it is likely that it is in need of lubrication. It would be best if you removed the mechanism and look to see if there is a physical obstruction. If not, oil it and let the oil soak in for a few minutes. Then try to gently work the mechanism back and forth a little at a time to see if you can get any movement. Once full movement is achieved, you can lube with white lithium grease and reinstall.
I have also found that one end of the gear will take all the wear, sometimes causing the window to not shut all the way. A simple trick to solve this is to switch the left side and right side mechanisms with each other. This allows the unworn section of the gears to be the part that is in use. It's like getting all new mechanisms without the cost or effort to find them.
Good luck with this, and let me know if you are successful.