This is apparently no widely reported--otherwise the hue-and-cry across Debian-KDE-land would be deafening :-)
What do I and the original reporter have in common? We both started out with a relatively recent Debian installer, he 7.4, I 7.5. And then, we both wanted to upgrade it. Bingo.
I do not know how he set his up but I used a multi-partition install and not wanting one-big-physical-partition, did not use LVM (probably an error!). Unfortunately, the Debian installer does not let me set this up the way I would want to do so. Throws 90% of the space to home and gives small partitions for everything else. So ...
/usr has little room for expansion. May rbind or symlink /usr/local off on that oversized /home or another platter. I remember doing all kinds of tricks like this when I had all of Debian on an 8gig partition. With one terra, I though all this stuff was behind me!
/opt -- no room for this at all. So ... same trick.
These have little to do with KDE, however. What about /var? This partition begins to fill up, with emails, with logs, etc., until it is pretty darned full. I have had the email system grind to a halt because humongous logs filling the /var partition. KDE still functioned, however. That was KDE3.
So, did the original reporter have separate partitions by the installer? How long before the issue started showing up? How much free space (if there be any minimum) does KDE require to log in and start the session? Problem is the /var has loads of smaller stuff. My one choice would be to symlink or rbind /var/mail (presently 40meg, too big, this may be in error due to kmail as well).
Cheap enough to try but would like some input here before.