Aha! Feroned has the solution that worked for me. Helix was giving me the -8201 error, and it had logged me out because the Line6 website was down at the exact time I tried to use it. (ie Even the Line 6 License Manager was reporting an HTTP error 500 when I tried to sign in, and visiting Line6.com just gave an Apache internal configuration error).
But even when the Line 6 website came back up, Helix Native didn't automatically fix itself.
So here is what worked for me:
* Log in again to Line 6 License Manager. It's okay that Helix Native doesn't show up in the list of Add-Ons. No need to deauthorize your machine.
* Launch Reaper and run the Helix Native plugin.
* In the bottom left corner of Helix Native, you will see My Account. Click on My Account, then click Sign In on the menu that pops-up:
* Log in to your Line 6 account
* Still didn't fix the -8201 error! But now quit Reaper, and restart Reaper, and add the Helix plugin again.
* You should find that Helix Native magically works now & logs you in straight away.
* If it doesn't, then if you've been trying to use the VST3 version, now try using the VST2 version instead. Once the VST2 version works, the VST3 version should also work again.
Wish I had that hour of my life back - glad I'm not a studio pro in the middle of a recording session - but I hope that info helps someone else!