Have you considered fixing the underlying problem: the bug limiting the size of your buf? Here's a solution if you can't.

If you remove the newlines, then you can just search for very long terms and replace them.

use strict;
use warnings;

my $file = '...';

open(my $fh, '<', $file)
   or die("Unable to open file \"$file\": $!\n");

my $reader = Reader->new($fh);
while (defined(my $line = $reader->get_line())) {
   $line =~ s/\S{40,}/.../g;
   print($line);
}
[download]

{
   package Reader;

   sub new {
      my ($class, $fh) = @_;
      my $self = bless([$fh, undef]);
   }

   sub get_line {
      my ($self) = @_;

      our $fh;  local *fh  = \($self->[0]);
      our $buf; local *buf = \($self->[1]);

      if (!defined($fh)) {
         return undef;
      }

      if (!defined($buf)) {
         for (;;) {
            my $line = <$fh>;

            if (!defined($line)) {
               undef $fh;
               return undef;
            }

            if ($line =~ /^\d\d:\d\d:\d\d /) {
               $buf = $line;
               last;
            }
         }
      }

      for (;;) {
         my $line = <$fh>;

         if (!defined($line)) {
            undef $fh;
            return "$buf\n";
         }

         if ($line =~ /^\d\d:\d\d:\d\d /) {
            return ((undef, $buf) = ($buf, $line))[0];
         }

         chomp($buf);
         $buf .= $line;
      }
   }
}
[download]

Output:

09:59:58 09/28/07 1 192.168.0.7 1.3.6.1.2.1.1.3.0 TimeTick 335604562 1
+.3.6.1.6.3.1.1.4.1.0 OID 1.3.6.1.4.1.9.9.383.0.1 1.3.6.1.4.1.9.9.383.
+1.1.1 Counter64 1119125906 1.3.6.1.4.1.9.9.383.1.1.2 String 07d7091c0
+9361400 1.3.6.1.4.1.9.9.383.1.2.14 String ... 1.3.6.1.4.1.9.9 String 
+... 1.3.6.1.4.1.9.9.383.1.2.16 String 192.168.20.60:3089 1.3.6.1.4.1.
+9.9.383.1.2.17 String osIdSource="unknown" osRelevance="relevant" osT
+ype="unknown" 192.168.0.23:139
[download]