The database – that stores all the data synced to the app – persists until the user logs out of the Axsy Mobile for Salesforce app. Once the user has logged in, the database will still be accessible even if the device is switched on and off again or the app is closed. 

For more information on Axsy's encrypted database system, please see this article: Offline-first User Experience

For more information on how to navigate the app to logout, please see this article: Logging Out of the Mobile App