Hi Brent,
I'm experiencing the same issue that Justin is describing on both iOS and Windows 10 (most recent versions).
Furthermore:
1) I still get the "Unable to Access the Internet" alert even though I have signed in previously. For good measure, I've also done the "Continue without signing in" while connected. If I drop my connectivity, I'm unable to "Continue without signing in".
2) When I choose to "Continue without signing in" when I do have connectivity, I cannot access my downloaded map. All I see is Esri content.
We were only testing the use of Explorer in the previous version (before running into the iOS 13 Enterprise logon compatibility issue when our phones updated). So I don't have a great memory of my UX with the previous version, but I swear that I was able to "Continue without signing in" without connectivity and access my downloaded map once I did.