Thanks for the info. I already found other similar answers, but nothing clear so far.
So according to your link, reinstalling the OS or maybe even renaming your computer, will use up a new authorization license. After you used up all your licenses, line6 support might be kind enough to reset them. But as far as I can see there is no guarantee this will happen.
This is especially annoying since I have Propellerhead Reason and I'm kinda forced to use line 6 products. Is there maybe another solution for me? I know I can use pod farm alongside with reason when I have a line6 interface. But I think I need to additionally register pod farm on my computer to get the amps and cabinets in reason itself. Or does my reason account count as its own device? So that no matter how many times I reinstall reason with my account it won't consume additional authorizations.