I don't think there's much Brian (the developer of KeePassDroid) can to, since it's Android that is denying the app write access to all SDCard except one application-specific folder.
When your phone is rooted, there are
a few things you can try to restore pre-4.4 behavior:
If you're not rooted, I would try putting the kdb file on the internal storage and see if you can write to it there (not sure, I only have JB 4.3).