I'm seeing something similar with Studio 1.13.0/Stardog 7.0.2
I can right click on the database and click "Take offline" and the database is successfully taken offline but when I right click and select "Bring Online" I get the error "Invalid database state. The database is offline (internal server error)"
The rocker button next to the label "Database status: Offline" will successfully online the database.
Can you try rocker button and see if you can online the database that way?
It's probably related to this report against 1.12.0 but it looks like the behaviour has slightly changed in 1.13.0