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: 
As edthethird said: best lay physical files on device external storage and read them on installation.
If the file content needs to be hidden from users just perform a simple encryption/decryption process.
At the age of 2020, it seems to me that `Shared Storage` is the way to go.

Android data and file Storage overview 

<https://developer.android.com/training/data-storage>

Shared storage of documents and files

<https://developer.android.com/training/data-storage/shared/documents-files>