Saving offline games

Whilst on holiday recently and offline, say on a plane, I played a few games and don't see them stored anywhere on iPhone or ipad. If I open the menu "Play", then press "completed games", there's nothing in there. I was hoping the App would save all my games on any Apple device and make them all available to any device once I'm back online? I don't see any mention of his in the online help at chess.com?

No, it sounds like you played offline against the computer. Those games are not saved. 

It has been suggested before but it is complicated because play versus computer allows takebacks.

I didn't think that you could get anything to work in an offline mode.