Since v2.0.2 (docker alpine version), the save button behaves very strangely.
Most of the time, it's disabled and one cannot save any modified dags. When it's available, running the dag makes it disabled again no matter what.
The only workaround I found to make the save button available again is either to edit and save the file externally or to disable/enable the dag by toggling the "live" button, and then never run the dag or move away from the edit window.

Let me know if you need any more info.