I figured it out. In case this helps anyone in the future...
As I mentioned in a previous post, I had installed a newer version of Logic Pro (10.7.x) at one time but found that it was buggy (possibly because the OS was not as updated). I reverted back to 10.6.3. To accomplish this and to allow myself to revert back, I renamed Logic.app to "xLogic.app" so the old version of Logic would stay in my Applications folder.
How this all played out with Mac OS and the App Store is not clear to me, but the result is/was that the App Store was aware that I had a current version of Logic Pro (not apparent to me because it was called "xLogic.app" on my system and therefore didn't offer any updates.
TL:DR check your applications folder to make sure you don't have more than one version of Logic Pro there, regardless whether you've renamed the alternate version of Logic Pro.