Had issues, but resolved myself

I also had issues with the latest version, with quotes not syncing or disappearing entirely. According to the developer they’ve been seeing an uptick in issues caused by some bugs Apple shipped in iOS9. They’re looking into it, but don’t have a fix yet. Suggested turning sync off, but click the iCloud sync button does nothing in the app, it’s permanently on.

Here’s how I fixed sync between the devices:
I went to my iPad which had the most complete library of quotes that wasn’t broken. I exported both a quotebook backup and csv backup and e-mailed them to myself. I then deleted both apps from my iOS devices. On my computer I went to iCloud > Manage > and deleted the quotebook data from iCloud. Wait 5 minutes for iCloud sync stuff to happen. Maybe restart your devices while you’re at it and make sure any quotebook data gets trashed. Re-install quotebook on one of your devices and then open your quotebook backup from email and it’ll import everything back into quotebook. Let it sync a bit. Install app on other device and confirm that things sync down. Make a change and make sure it syncs across devices. Nice! The old “unplug it and plug it back in” trick. Works every time! Sync seems to be reliably and quick compared to my previous experience, so far so good.

BVP663 about Quotebook — Notebook for Quotes