Klipper doesn't store new clipboard data without a proper KDE shutdown. It should store it as it goes and without risk of loosing old data. Instead of 'Save clipboard contents on exit', something like 'Save clipboard contents after copying for future sessions'. Right now if my KDE session were to end impproperly (like the power button is held down for 10 seconds, etc...) any new data in the clipboard copied after the last proper shutdown is lost. Possibly related to Bug 64257 Klipper does not restore right clipboard data
This is implemented since Plasma 5.3. Once you upgraded to Debian Testing you will have a save after every clipboard change. *** This bug has been marked as a duplicate of bug 343333 ***