My son was having this issue and we tried all of the stuff recommended above to no avail but ended up resetting his phone and downloading his last back up from the cloud (thankfully it backed up last night) and the notes came back just fine. Highly recommend going this route if you have a recent backup from before they disappeared.
The method above (checking outlook through safari) was just posted after we got his notes back and moved from Hotmail to the icloud, and we tried it just to see and that worked as well. For that method you go to outlook and look at the area where you select a mailbox (inbox, sent, etc.) and there should be a section that says notes.