I always found it strange that I could open Konqueror, resize it, and close it; only to have it appear again at the original size the next time it launched. I had checked the Configure Konqueror options under the Settings menu before, but never found anything. It was only after reinstalling Kubuntu this weekend due to a failed hard drive that I discovered why window size wasn't being saved.
The solution is under the Settings menu, but through Configure View Profiles. Simply select "Save window size in profile", hit Save, and you're done.