Im not an expert on the FP3 but own one and have some experience with it. In my experience you can auto tune any map that has been saved except for the stock map that was originally on the bike. So yes, you should be able to continue auto tune on a finished map. My stock map says read only and never tried to auto tune it so not sure if there is a way.

My FP3 app does the same with a iPhone 7. You can double tap the home button to get the app back, but it starts from the beginning though. It doesn’t pick up where you were at before in the app. It’s the only app that I have that behaves like that.