Question: I am keeping some application meta data in `SharedPreferences`. Whenever I uninstall the application and reinstall it, the `SharedPreferences` are deleted.

Is there any way to get that to remain, so that if the user does an uninstall and reinstall, they can recover their old data?

Answer: 
One way to do this would be to store the user data on a server. Then when the user re-installs the app or installs the app on another device, they can "sync" their user data. That would just be a small HTTP download of the data, likely stored in JSON, which you would then parse and write into the SharedPreferences.

If you don't want to maintain your own server, you could use a cloud service like Dropbox. This is how the app 1Password Reader works.
sharedPrefs and DBs are removed when you uninstall. You would have to write outside of the app (sd for example).