package My::DBI;

my $dbh_static;  # fester Handle
my $dbh;         # temporärer Pointer, wird nach jedem HTTP-Request gelöscht.

sub dbh {
  $dbh ||= _connected_dbh()
}

sub _connected_dbh {
  unless (is_conneced($dbh_static)) {
    $dbh_static = DBI_>connect(...);
    # init $dbh_static
  } 
  return $dbh_static;
}