It is very common to have in Thunderbird accounts inactive or used for reasons other than the regular sending and receiving email, etc.

Thunderbird may still try to connect to receive email from such accounts when you press the “Get Mail” button!

To have Thunderbird ignore these accounts completely unless you decide manually to receive email, go the settings of each account then to the “Server Settings” section and remove the check marks from the options to “Check for new messages at startup”, “Check for new messages every x minutes”, “Automatically download new messages”.

Then press the Advanced button and remove the check mark from the option to Include this server when getting new mail.