Is RaiseError set, or barring that, are you checking $h->err and/or $h->errstr after each database operation? It's unusual behavior for DBI to disconnect without any reason.

If all else fails, there is DBIx::Connector which can quietly handle ensuring that you always have a valid database handle available, but that's not a real solution for this problem; I would sure want to know why it's happening in the first place, and error checking might just divulge such information.