Hello icon41gimp,
From what I read, it seems like the forums log you off from a device when you log in to a different one.
Not sure how to resolve this just for the forums, but I think you could find certain tools such as KeePass useful (not just for this site, but for many). These store your passwords and log you in automatically to any services you configure, by using the Auto-Type feature. The only thing you will notice is a small delay while KeePass does its work for logging you in:
KeePass:
https://keepass.info/
KeePass Auto-Type Feature:
https://keepass.info/help/base/autotype.html
This software is completely free, so it is worth giving a try.
Regards!