my $entry = "";
while (<LOGDATA>) {
   if(/^($monthRegex)\s+d{1,2}\s+(\d{2}:){3}/) {
      $result = &handleEntry( $entry ) if $entry;
      $entry = $_; # unless you want to ignore some of'em
      # in which case: $entry = "";
   } else {
      $entry .= $_ if $entry;
   }
}
$result = &handleEntry( $entry ) if $entry;
# and replace the "foreach" loop in the previous version
# with "sub handleEntry { ... }"