Some of my notes don't sync through iCloud, why?

Some of my notes don't sync through iCloud (even if they're in the iCloud category in notes), and after getting a new phone when switching carriers, I lost some important work notes. I tried restoring from an earlier backup, but the notes app was completely empty after the restore. I suppose the notes data wasn't stored locally through the backup and it was getting them all from iCloud again after syncing.

I have now switched to iWriter for note taking, as it doesn't seem to have that problem. Sometimes I would create a new note on either my computer, or phone, and the note wouldn't show up on the respective other device. I made sure to check, if they were in the iCloud category in notes. I went through other threads in the support forum but nothing I found directly addressed this. However, I saw something that gave me the inkling that it may have to do with how I use my email addresses. At some point I stopped using the native mail app for my main email address and switched to Mailbox App. Could that be the cause, that maybe some notes I created were somehow associated with my main email address and therefore they wouldn't sync after I deleted that email account from my mail app settings? They were still on the phone, they just didn't sync.

Why won't all the notes sync?

Thank you, any help would be appreciated (especially seeing as I have some sensitive work information in those lost notes that I desperately need)!