If you accidentally close that Fastmail tab, just open another one. You will lose nothing. You can be logged into Fastmail from several devices simultaneously

If you accidentally close that Fastmail tab, just open another one. You will lose nothing. You can be logged into Fastmail from several devices simultaneously. And I often have several Fastmail tabs open at one time. No problem at all. The only thing better than Fastmail webmail is the Fastmail app for iOS.