This is only occurring in Chrome browser 109 on different devices with v4.138.3.
Version 4.138.3 extension in Firefox has no issues staying logged in after closing and reopening the browser.
4.138.3 in Chrome 109 (Doesn’t stay logged in)
4.138.3 in Firefox 99 (Stays logged in)
Tested version 4.130.0 in chrome 91 portable and it works properly (Stays logged in).
I’m considering uninstalling 4.138.3 and installing the latest version 4.139.0.
If that doesn’t work, I will install version 4.130.0.