Thunderbird has removed support for the broken versions of SSL. Perhaps kmail has not.

Which broken SSL, on the client or on the server?

Is there a log file that I can open to see if the SSL version is accepted on not?

All SSL actually. TLS has replaced it for years. Just us users still call it SSL. HTTPS is TLS not SSL as well apparently.

Logging is explained here. https://wiki.mozilla.org/MailNews:Logging

I got the following in the log :

6712[1611600]: 7603800:imap.tzone.org:NA:CreateNewLineFromSocket: 1 NO [UNAVAILABLE] Maximum number of connections from user+IP exceeded (mail_max_userip_connections=10)

If close and reopen both thurderbird, it works. I had a max connection of 5 for each, it seem that thunderbird is leaking connections.

Sounds like everything is working as it should, just not as you expect. If you want to dial down the concurrent connections. Right click the account in the account pane. select server settings and the advanced button and reduce the default 5 to something else. This is not new however, it has been an IMAP standard for Thunderbird since before I started using version 2. Multiple connections speeds up the synchronization process. So I never looked at it as a possible issue. Did you perhaps get an iphone/Smart phone/Tablet as well into the mix that brought the issue to light for you?

The phone has been there for more then a year. But I was having the message when the phone was off, with just one Thunderbird running and the other starting I should not have been over 10 (with the value of 5). I still believe thunderbird is leaking connections.

If you can log such an event I am sure we can get the attention of a developer through filing a bug. But without a steps to reproduce so they can see it in action then nothing will really get done. It is hard to fix something you do not see broken. You might find someone already has a bug for that if you search bugzilla. https://bugzilla.mozilla.org/ But I just do not have time to look today.