Just want to chime in and say that I had this happen to me as well. Signing in with the "stay signed in" option unchecked worked finally, but I had to manually clear cookies/local storage then login from the main fastmail.com home page.
Definitely super frustrating to keep getting logged out on a regular basis because I can't check that box without breaking the entire app. Is there any progress on figuring out the cause? I only have the Bitwarden extension installed, nothing else as far as extensions go.