The power windows do not run through a relay, (other than a main safety relay in the dash panel). Power comes from the fuse panel, to the switch, and then to the motor.
What usually happens, is the commutator on the motors gets a bit oxidized, and does not make good contact with the carbon brush. If your car sits for long periods, or you do not run the windows up and down often this is how the commutators get "dirty", and more-so if you live in a high humidity area.
One of my windows, driver main, occasionally stops, as you note, and what I do, is to hold the button up or down, depending on where the window is, and open and close the door firmly. That usually causes enough jar to make the connection between the brush and commutator. When I do use my car for shows, etc., I always run all the windows up or down, open or closed, to clean the commutators and brushes, and have no problem.