If you have an email account which has been deactivated, you want Thunderbird / Icedove to stop checking for new messages each time. But you do not want to completely remove the account because you like to keep the old messages and maybe it’ll be reactivated soon.
So do this (tested in Icedove 17.x): Go to Menu – Edit – Preferences, Advanced section, General Tab, click on Config Editor button.
Enter mail.server.server*.name as search string and find the number corresponding to the email account you want to disable; let’s assume it’s the number 5.
Now enter mail.server.server5.check_new_mail (replace 5 with the actual number that works for you) and set that property to false.