I found this on the XLN FAQ page:
If a product suddenly goes to trial mode, it means that something in your computer triggered a change in the Computer ID (perhaps a software or hardware update). This in turn deauthorizes your product. This is easy to fix:
Login to your user account and go to My Account -> My Computers
So I did, and it shows two computers registered, both identical. And it warns that "You currently have your maximum amount of active computers. Remove old unused computers if you need to register a new computer."
There was no indication which "computer" was current, so I click the Edit button to see if maybe there was a datestamp. There isn't, but they do show different computer IDs. I was able to match one of them to the current computer ID (click on the Addictive Drums logo for the About page) and delete the old one.
I hate this kind of copy protection. A few years ago I had to replace my computer's motherboard, and half of my instruments and plugins had to be re-authorized. I'm sure glad hardware synths don't work that way.