Update November 10th, 2020:
We have been made aware that our recent Android Headspace app update affected the app's ability to function offline. We do apologize.
Please note that this issue only happens if you shut the Headspace app fully prior to switching to offline mode. A workaround for this issue is to leave the Headspace app running in the background prior to switching to offline mode.
Our engineers are currently working on a fix for this and it should be released with the next app update. Thank you for your patience.