Hey everyone- just an update. I noticed that there was a new version of the neo note app for my iPhone, so I downloaded it last night. It didn't make any real difference UNTIL I deleted the app entirely, then reinstalled it.
My offline sync works perfectly now! As long as my pen is on (I've got it set to auto on, so it starts up as soon as I start writing), it captures everything and syncs when I connect it to the app.
The only issue I have now is that the pen connects automatically as soon as the app starts, but if I keep the app open, then turn the pen off, then back on again, it won't automatically connect. I have to connect by pressing the icon on the top right of the screen in the app. But now that it captures offline content, this isn't that big of a deal.
If anyone is having problems, just delete the app and download it again.