Q: I am trying to update to 9.3. In settings it show as downloaded, but when clicking install now, etc, I get a message that it cannot verify because we are no longer connected to the Internet (which we actually are). Help!

Apple has pulled the iOS 9.3 update for older devices (iPad Airs and previous, iPhone 5s and previous) due to problems with Activation. See these articles for details and possible workarounds.

http://www.imore.com/apple-working-ios-93-fix-older-iphone-ipad

https://support.apple.com/en-us/HT206203

A new build for the iPad 2 is now available that does not require the Activation step. A new build for the other devices is not yet available. You will have to wait until Apple issues a new build for the Air. If yours is working ok at the moment you are one of the lucky ones.