Thanks again for your reply. I had actually performed all of your suggestions before my first post on the forum, but I do appreciate your input, especially your suggestion about checking Configuration > Item Wait Time.
I installed the latest version of the software in question on a test PC, rescanned that Asset in Lansweeper, and the software shows up within Lansweeper.
We have less than 10 users who are using this software for years now, but there have been issues as they've upgraded this particular software time and time again.
The software is also one of those packages that ONLY shows up in Programs & Features when logged in as the user who installed it. I tested this on my recent installation, and it does NOT show up in Programs & Features for another user account, or even for the Domain Administrator (yet I'm using the Domain Administrator's credentials for Lansweeper, which does correctly scan the software as being installed on this particular PC!).
So I'm just going to attribute the issue to a quirk with that software, and probably not worry about it any more.