I've had the problem of kmail locking up every once in a while for years, but it's happened 3 times in the last 3 days. And it's not just a case of closing it and reopening it: there are sub-processes which, if killed, make it so that kmail won't work until the next reboot.
So what happens ? It checks for mail on my pop3 accounts and it never finishes. I can keep using it in the meanwhile but no new messages come in.
Unless someone can explain how to restart kmail properly, I have to reboot the system, which I am loathe to do (it's a server for a lot of things).
$ ps faux | grep mail
user 2865 0.0 0.6 340156 48536 ? Sl Mar13 0:02 \_ /usr/bin/akonadi_agent_launcher akonadi_maildir_resource akonadi_maildir_resource_0
user 2866 0.0 0.3 339660 24676 ? S Mar13 0:00 \_ /usr/bin/akonadi_maildispatcher_agent --identifier akonadi_maildispatcher_agent
user 2867 0.0 0.6 625308 48880 ? Sl Mar13 0:01 \_ /usr/bin/akonadi_mailfilter_agent --identifier akonadi_mailfilter_agent
user 3451 3.0 1.4 2158064 115224 ? Sl Mar13 27:01 /usr/bin/kmail -session 10e5cedc67000136319936300000026520023_1363201973_899610