I'm sure someone will post an efficient regex, but in the meantime you can try this. Still a bit ugly, lines are joined then split on the HR tags.

YuckFoo

#!/usr/bin/perl

   use strict;

   my ($line, @keep);

   for $line ((split(/<HR>\s+/s, join('', (<DATA>))))) {
      if ($line =~ m{\d+\s+is\s+good}) { push (@keep, $line); }
   }

   for $line (@keep) { print "$line\n"; }

__DATA__
<HR>
1 is good<BR>
useless data<BR>
useless data<BR>
useless data<BR>
useless data<BR>
<HR>
2 is not good <BR>
useless data<BR>
useless data<BR>
useless data<BR>
useless data<BR>
<HR>
3 is good<BR>
useless data<BR>
useless data<BR>
useless data<BR>
useless data<BR>
<HR>
4 is not good <BR>
useless data<BR>
useless data<BR>
useless data<BR>
useless data<BR>
<HR>
[download]