I'm not a big fan of popup notifications for non-critical events (and running out of disk space for logs isn't critical, IMHO) - they get in your way when they shouldn't, and if you click them away to continue the task at hand, you easily forget about the error condition. Something non-modal would be better, perhaps a mechanism leveraging the status bar, or something similar to the notification bars web browsers (Firefox, IE, etc.) use these days.

Then again, I'm not sure this notification belongs in Konversation to begin with. Konversation is not the only user of disk space, and implementing such notification in each user quickly gets out of hand. Maybe this is really more of a job for the KDE workspace. And even if it isn't, the design of an unintrusive error notification mechanism should probably transcend Konversation as well.

I happen to be in agreement with Sho on this one (OMG!), especially since kdf, i.e. K Disk Free, has this functionality. If you really want to know if you're about to be out of diskspace, you can run the kwikdisk  applet (which lives in the statusbar). If my memory serves me correctly it comes complete with annoying popup, not only telling you when you're out of disk space, but also when you're almost out of diskspace. 
Or, we could just steal the code. Not everyone installs kdeutils after all :-)

There's some renewed discussion about adding "you're running out of space, bud" notification to the Plasma shell in KDE 4, which brings me back to this report. I continue to believe that this is something that ought to be implemented in the workspace, rather than clutter individual apps. As for Konvi behavior when running out of space, it will obviously fail to write logs, but it won't crash (I run out of space all the time, and so far it has always handled it fine). Closing.