A question regarding the connection pooling feature of application server.

When we have a scenario where in the database goes down for some reason (network failure, database explicitly shutdown..), do we have to re-start the application server so that the applications continue to work fine? Or is it that application server would ensure a "plug-n-play" model where in applications accessing the database would continue to work fine without a server restart after the database is brought up?

My understanding is that we would have to restart the application server when the database goes down - please correct me if otherwise.