I'd do something like this:

my $date;
my $lastdate = '';
my $logdata = '';
while ( <LOGFILE> ) {
   $date = extract_date( $_ );
   $logdata .= $stuff;
   if (length $lastdate and $lastdate ne $date) {
     print_report( $lastdate, $logdata );
     $logdata = '';
   }
   $lastdate = $date;
}
print_report( $lastdate, $logdata );
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That's the rough idea, anyway. Instead of extract_date you may have a parse method that returns a date and whatever else you want from each line. E.g.:

  ( $date, my $stuff ) = parse( $_ );
  $logdata .=  $stuff;
  # etc.
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Also, barring some crazy scheme for the date, the test in the loop could be simplified to

if ( $lastdate and $lastdate ne $date ) {
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Another possibility, if you want to keep everything within the loop, is to use eof to test for the end-of-file condition. Then the above would become:

my $date;
my $lastdate = '';
my $logdata = '';
while ( <LOGFILE> ) {
   ( $date, my $stuff ) = parse( $_ );
   $logdata .= $stuff;
   if ( $lastdate and ( $lastdate ne $date or eof LOGFILES ) ) {
     print_report( $lastdate, $logdata );
     $logdata = '';
   }
   $lastdate = $date;
}
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