I have a non-Perl answer but it's probably the best answer that you will receive.

Install pgbouncer and point the app at it. Before you restart the database, connect to pgbouncer and pause all connections to that database. Then you can restart the database. Once the database comes back up, unpause the connections in pgbouncer.

PostgreSQL restart with PgBouncer without losing client connections (YouTube)

In reply to Re: Handle DBI connection lost by Mr. Muskrat
in thread Handle DBI connection lost by bash

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