Version:           1.12.2 (using KDE 4.3.2)
OS:                Linux
Installed from:    Ubuntu Packages

I have made some networks trace, and I think I understand why kmail seems to stay blocked sometimes, with imap account, TLSized or not.
 When you stay a long time, it is higly probable that the imap account seems to be unreadable. kmail seems to work without end. But, it is not true with all imap account. for instance, gmail accounts don't suffer with kind of problem.
This is due to the way that kmail is dealing with imap connection. It seem to assume that imap conection must be endless. This not true. There is a lot of situation where this hypothesis is incorrect. For instance, if you freeze your laptop, kmail will not be able to maintain the imap connection open, and the server will close it.
 Other case, there is a lot of firewall that have a timeout for tcp connection.
Gmail deal with this kind of problem using the following algorithm: if the server receive a tcp packet that doesn't correspond to a living connection, then it emit a tcp reset. Then kamil reinitiate a new imap session, and it is working.
 But other servers don't work this way. They don't emit tcp reset. They act as there is nothing. It is a simple security measure.
And in this case, kmail try endlessly to reemit the same tcp packet.
It should be a timer that induce the reinitialization of the imap connection.