How do you define the end of the exception? I'm going to assume you want to insert a blank link before the first line that doesn't match in a group of successive matches.

my $blank_needed = 0;

open(DIFFR, "javaex.log");

while (<DIFFR>) {
   if (/at / || /xception/) {
      chomp;
      print LOGFILE "$_,\n";
      $blank_needed = 1;
   } else {
      print("\n") if $blank_needed;
      $blank_needed = 0;
   }
}
print("\n") if $blank_needed;
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