Typically, when a signal is too weak or absent to sync, I find that your screen shows blank with your logo at the top and after (consistently) ~20 seconds, the app closes and reverts to the iPhone icon page.
Doing as you asked the app behaves correctly. Apart from all the tasks being present there is a notice at the bottom stating there is no connection.
FWIW, I can tell you for certain that the preceding does not resemble what I periodically see at 32003 Ellingwood Trail, Evergreen, CO 80439.
I'm thinking that the airplane mode tells your app absolutely no service and your app responds properly to the definitive no. OTOH, my referenced location's connection is sometimes present, sometimes not and when present that condition is in various levels of ATT weak--never any better. I'm thinking your app may be getting confused during that 'weak try and grab a connection decision moment', timeout and end up back at the icon screen.
Just a thought.
Oh and about those previous posts. Being new to any smartphone and apps it took a bit to understand the demarcation between your app (which does a fine job) and the syncing app (which also (now) does a fine job)