yes, that's probably it. before you separate the two layers of the windsavers, look to see if there is any darkened area between them that disappears after you separate the layers. that's the location of anything that's making them stick and what you would be cleaning away using tom's technique. sometimes it's a bit of 'syrup' formed by the moisture in your breath combined with sugar from drinking soda or coffee, but it could be other things.
i have exactly this problem with my suzuki G48, same draw note. after each fix, i'm able to play for a longer period of time before it happens again.