An application that has no access to the external network service should not panic. This should be expected as networks tend to fail. I would wrap the error and pass it further.
Consider the following scenario. You have multiple application servers connected to two database servers. You are upgrading the database servers one at a time. When one is turned off half of your application servers panicked and crashed. You upgrade the second database server and every application server is gone now. Instead, when the database is not available just report an error for instance by sending HTTP status 500. If you have a load balancer it will pass the request to the working applications servers. When the database server is back, the application servers reconnect and continue to work.
Another scenario, you are running an interactive application that processes a database to create a report. The connection is not available. The application panicked and crashed. From the user perspective, it looks like a bug. I would expect a message that connection cannot be established.
In the standard library it is accepted to panic when an internal resource is not available. See template.Must. This means something is wrong with the application itself.