I use old.reddit.com exclusively (automatically enforced by a browser extension[1]) and haven't experienced unexpected logouts.

[1] https://github.com/tom-james-watson/old-reddit-redirect

you’re not alone and it’s a common complaint. along with the complaint that toggling “opt out of redesign” is constantly coming untoggled randomly and without warning. This doesn’t even happen between browser sessions where one would think a cookie got dropped, it can happen simply between pages. one moment you’re using old reddit, click a comment link, boom..you’re back on the redesign and having to change the setting again.