Usually this occurs when your email server drops the authentication and you need to reauthenticate. 

First you will need to remove and re-add your account in Mailbird.

If you use IMAP connection, all your emails will be downloaded back to Mailbird after you add the deleted account back, you will not lose any data. If you use POP3, please contact support for further details.

How to check your email protocol:

Go to Menu -> Settings -> Accounts -> Double click the affected account and check the port number.

995 and 110 are the ports for POP3. All the rest are IMAP.