Mozilla Thunderbird sets the default number of maximum allowed IMAP connections to 5. You can connect to the IMAP server as often as you want however you may be restricted in the number of simultaneous connections that can be open during that connection.
If you are getting the following error message:
"Unable to connect to IMAP server. You may have exceeded the maximum number of connections to this server. If so, use the Advanced IMAP Server Settings dialog to reduce the number of cached connections."
To resolve this you will need to change the maximum number of connections in Thunderbird. This can be done from 'Tools - Account Settings - [select your account] - Server Settings - [Server Settings section] - Advanced - Maximum number of server connections to cache - [Enter 1] (Change the maximum number from 5 to 1).
