Microsoft activation typically ties an install to a specific computer, to prevent people from activating once and then just cloning the hard drive.
When you upgraded Parallels, it may have changed the hardware that was exposed to the operating system. This caused the license manager to believe that you had indeed moved S&T to another computer.
People do make changes to PC components (installing more memory, a new video card, a new hard drive, etc.). So there's a certain tolerance built into Microsoft activation, where you can upgrade some percentage of your computer without triggering reactivation. Apparently the Parallels release version exceeded that tolerance.
Running the beta probably exacerbated the situation. Typically, software companies will try to avoid causing problems when you upgrade their software from one release version to another. But with betas, anything goes.