One of your remotes has reverted to the billion code technology. You need to purchase a remote with the same model number as your old one. You will find the new remote will work with one of your old ones and not with the other. Remove the batteries from the bad remote and discard it. Otherwise it may cause problems down the road.

I worked for a guy that did garage doors for ten years. According to him NEVER use anything from sears or craftsman when it comes to garage doors, the are equal cost alternatives that are much better and safer

Here is a link that might be useful: Tuff PLay

We have two Craftsman 1/2 HP GDOs, with three-button remotes and keyless pads. (Model 139.53982SRT / Part 41A5483-2). One of the GDOs will not hold programmed codes on remotes or keyless for more than 24 hours. Hence, I use "learn / re-set" process each time we leave the garage on that side. Any hints to repair, or just time to replace (installed in 2002)?

Sounds like your logic board is bad. The part number is the number you gave. It's almost a toss up - repair or replace depending on if you can do it yourself.