First of all I'd recommend switching over to this tutorial, as it was updated to reflect some changes in the SQLite libraries (for example, they're all now accessible via NuGet, no more building from source).
I'm not entirely sure why your database is being deleted and remade on each debugging, but you cannot write to installation storage (i.e. your solution) during runtime, only app storage. If you want to browse the app storage of one of your deployed applications, whether it be on an emulator or on a device, you can use a tool like WP Power Tools.