$str =~ /\G(##.*?)(?=(##|\Z))/gs
might be faster, but it's probably the same.

$str =~ /\G(##(?:(?!$##).)*)/gs
is something to try.

Taking advantage of the fact that '##' is at the begining of a line might help greatly.

But you don't even need a regexp. Use index, which is lightyears faster:

my $sep = '##';
my $sep_len = length($sep);

my $last_pos = index($str, $sep);

for (;;) {
  my $pos = index($str, '##', $last_pos + $sep_len);

  my $rec;
  if ($pos < 0) {
     $rec = substr($str, $last_pos);
     last if not length $rec;
  } else {
     $rec = substr($str, $last_pos, $pos-$last_pos);
     $last_pos = $pos;
  }

  my $rid = substr($rec, 19, 10);
  print "$rid: " . ($keeplist{$rid} ? 'y' : 'n') . "\n";

}
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You can even avoid copying stuff into $rec:

my $sep = '##';
my $sep_len = length($sep);

my $last_pos = index($str, $sep);

for (;;) {
  my $pos = index($str, '##', $last_pos + $sep_len);

  my $rec_pos = $last_pos;

  if ($pos < 0) {
     last if $last_pos == length($str);
     $last_pos = length($str);
  } else {
     $last_pos = $pos;
  }

  my $rid = substr($str, $rec_pos+19, 10);
  print "$rid: " . ($keeplist{$rid} ? 'y' : 'n') . "\n";

}
[download]

Update: Added code. Untested.