One day, I found that there was no new email coming in to my Mozilla Thunderbird email client for quite a long time, but I could still receive new emails from the same server with my smartphone.
I looked into the Error Console of Thunderbird by going to Tools > Error Console (you can also press the hotkeys Ctrl-Shift-J to go to the same place) and found this error message:
A search in the Internet informed that Mozilla Thunderbird version 38.1.0 and above will block the connections to any mail server using weak ephemeral Diffie-Hellman (DH) keys by default, therefore it can no longer retrieve new emails from the affected server.
Bear in mind that by default, Thunderbird is set to automatically update itself from time to time, so your version will eventually be updated to version 38.1.0 and above.
Blocking the weak Diffie-Hellman key exchange is in fact a security measure against Logjam attack against the TLS protocol. You can click here to read more about this Logjam attack.
Affected email servers including older version of Zimbra Collaboration Suite. Click here for more detail.
While waiting for the mail server administrator to fix the problem at the server side, I applied the Disable DHE 0.1.2 Add-on by Mozilla to my Thunderbird, and it can now continue to receive new emails from the server.
To apply this add-on to your Thunderbird email client, click on the link above to go to its download webpage.
Then, click on the "Download Anyway" link and save the file disable_dhe-0.1.2-fx.xpi in your computer.
After that, go to Tools > Add-ons in Thunderbird, pull down the menu button on the left of "search all add-ons" and select "Install Add-on From File..." to install this disable_dhe-0.1.2-fx.xpi into your Thunderbird.
Restart Thunderbird and check if this fix works for you as well.