Let’s say I finish a 30 mile ride and I want to close and save that because it’s a ride I do regularly and I like to compare them over time. So I want to save that and then ride another 20 miles. Why can’t I figure out how to do that? The app closes and I have to start it again. There’s gotta be a way.
No, it is not possible.
ZWIFT is stupid that way 
You have to close and restart the app.
One of the most asked for features, vote for it here: