Same thing is happening to me on both iPad and iPhone after iOS 6.1 upgrade! In fact, I noticed that if I try to start a new note, as soon as I minimize the keyboard and it starts to synch, the note disappears. I can't even create a new note and keep it! Same thing happening on both devices, so I think it's a bug. I was able to find my old notes though, just by luck. You'll have to log into a computer rather than your device though, and don't ask me why. Here's how to find:
1) go to settings on your device and look at Notes.
2) look at what it lists as "default account". That's your email account where it should have saved copies.
3) log onto that account on a computer. Can't see it on your device - at least I couldn't.
4) in that email account, you should see a folder called Notes. In there, you'll find your saved notes. (Again, for some reason, this folder doesn't show up in my email folders on either mobile device.)
I'd be interested to know if you also experience the same problem creating new notes.