Craftsman Garage Door Remote Problem

Hi all,
Just wanted to pass along a recent experience with my late 80's-vintage Sears Craftsman garage door opener with the Security+ feature of rolling codes for the remotes. Similar problems have been posted here before but I didn't see a clear solution that someone had tried and it worked for them. Here's my story:
I've got two remotes for the opener and both worked fine for years. A couple of months ago one of the remotes stopped working. First thing I did was replace the battery. Didn't fix it.
Next, I dug out the manual to refresh myself on how to program the remotes for the unit. I put the opener into learn mode and tried to program the previously dead remote: no luck. Next, I tried dumping (resetting) all codes in the opener by pressing and holding the learn button for several seconds. What I discovered after that was that I could get either remote to program successfully, but only one at a time. If I reset all codes and programmed the "good" remote first, it would work fine but I could not get the opener to recognize the second remote. Likewise, if I reset the opener and then programmed the "bad" remote first, it would work fine but I could not get the opener to now recognize the second "good" remote! I tried this several times with slight variations thinking that I must be doing something wrong. No luck.
Cutting to the chase: I bought a replacement Liftmaster Security+ remote from the web and it works like a champ. I'm back to having two good remotes-- one old, one new. Something must've happened to the code sequence generator in that one old remote. Problem solved and I didn't have to spend $200 and a Saturday replacing the entire garage door opener. :)

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