I had the same problem with the driver's window. It was making a straining noise, also the window was squealing/making noise when it went up and down. Took it in for service, and of course, service advisor says that the regulator is nonserviceable, and more than likely it is the motor.
I finally got tired of it and bought the regulator/motor online and had them replace it.
My feeling after I got the old parts, was that the grease in the regulator, and all moving parts that had been greased, had no grease, or the grease was dirty and congealed and was putting a strain on the motor. However, once it had gotten to that point, it became nonserviceable because the metal parts had scored a nice "engraved" line in the moving parts and was causing the regulator to squeal as it moved the window up and down. Whether or not the regulator could have been regreased and put back into service for any length of time, I doubt it. AFAIK, the motor is ok (I did not test it - I kept it, but tossed the regulator as it was basically trashed.) My feeling is the regulator was causing the straining noise (on the motor).
You might try to regrease the regulator if you are inclined to fix it yourself, but it has to be removed from the door. I attempted to regrease the regulator without removing it from the door, and had some success, but the straining noise and squealing came back.
My passenger window is now doing the same thing. But I ain't working on it, and I plan to have the regulator/motor replaced after the first of the year.