The old grease no longer resembles grease, it's all dried up and will stop parts from moving. I don't know how long it takes for the contacts to cool down. What you can do is when the window stops moving just keep the switch engaged and wait for them to make contact again. You won't hurt the motor since no current will be going through it.
What I'd to do diagnose the problem is remove the window itself, leaving all the other hardware in place to see how it functions. Then remove the motor/regulator and see how easily the window moves up and down the window channels. That way you can narrow down if it's on the window side or motor/regulator side ... or maybe a combination of both.