One of my LiftMaster garage door openers (1/2HP, Model 1205A, MFT 1999) stopped working after 10 years.  Upon first glance, I saw white dust had accumulated in the Up/Down travel adjustment holes. Upon removing the casing, the nylon drive gears had failed (the drive gear that turns the sprocket had stripped).
This past weekend I fixed the opener in about three hours and I highly recommend the: Liftmaster Gear and Sprocket Assembly Kit Part Number 41C4220A.
I also bought Sears Craftsman Liftmaster Garage Door Opener Gear Kit – Part #41A2817 as well because my house has two LiftMaster openers. Â But I found the sprocket solution to be better in this case as I could just drop it in. Â I now have the extra stripped sprocket which I can use with the extra part kit to replace the stripped gear and reuse it on my second opener when and if that fails.