Mail goes offline spontaneously in Big Sur

[macDISH]

Mail has become unusable for me in Big Sur as it goes off line almost every time the computer (MacBook Air 2020) is unused for even brief periods. The only way I have found to get Mail back on line is to reboot the computer. Turning WiFI on and off, quitting and restarting mail does not help. The only reliable way I can access my email accouiunts on the MacBook is  via webmail, which to me suggests the problem is with Big Sur and Mail, rather than with my ISP.

[jchuzi]

In Mail, go to Window > Connection Doctor and see if anything helps.

[macDISH]

Connection Doctor logs will take some time to go through. When Mail goes off-line, connection doctor merely notes that it is not connected to either POP or SMTP for either of the two accounts.

[Xairbusdriver]

I'm sure that is frustrating!

In Mail prefs, Accounts, do you have "Automatically manage connection settings" checked?
If not, what ports (incoming and outgoing) are used?

Signal Strength questions:
How many wifi 'bars' show on the Air, at least where it is normally used?
Does orienting the Air differently affect the number of bars?
How many walls between the Air and the WiFi transmitter?

I'm not familiar with the MacBook Air, but there may be some System Prefs that you can change/adjust:
Power Saver: What are your settings?
Network: Settings?

Connection Doctor also has an option to show/hide details. There are also Console logs that may show why the connections were not made or why they dropped. Just check the "Log Connection Activity".