I have had this lock for a few months now and loved it right until tvOS10 and iOS10 came out. Now nothing works like it did. I still have the separate codes for separate individuals and the scheduled access for my cleaner works great. But the app on my phone no longer connects to the lock unless I physically go over to the lock and touch it (manually locking/unlocking it from inside the house, or touching the 'Schlage' button on the outside). My Apple TV is set to never go to sleep. My home wifi is great. I've installed the new firmware on the lock. But I can no longer remotely control the lock or access its history.
In addition, and I'm sure this is related, in my Apple TV the HomeKit login is no longer shown in iCloud settings.
Someone else wrote about the other problem I've been having: automation doesn't work. On iOS 9 I had the Elgato Eve app setup to automatically unlock my house according to a geofence. That was great. Then under iOS10 it stopped working automatically and I was getting a notification which I had to manually confirm. Now with the tvOS release I have no automation at all.
Ack! I just upgraded my firmware and my remote use is now dead too. Like you, the keypads work but the app is disconnected. I've held off on "re-pairing" in hopes that an update is coming soon that will fix it.