I would recommend a slight rethink of the problem. There are two things (as you've explained it) that need to happen:

1. We need to capture lines that aren't "THIS IS A BREAK" and process them.
2. We need to know when we've hit a break line.

I would suggest that you change the logic to reflect that. Right now I don't see you ever checking at all for the break line, which is certainly not going to work.

Try it this way (pseudo-code so you can get the practice writing the Perl):

my @captured;
While I still have records:
  Is this a break line?
    Y - check_for_more_breaks(@captured)
        @captured = ()
        next item
    N - save line to @captured
Anything left in @captured?
   check_for_more_breaks(@captured)

sub check_for_more_breaks:
  # Your actual processing here is unclear; I've taken
  # a guess at it.
  my @subgroup;
  my $last_sequence_number;
  for each line:
     extract the fields
     is last_sequence number defined?
         N - save this one as the last sequence number
             save the current data of interest in @subgroup
             next
     else is there a gap in the sequence numbers?
         Y - summarize(@subgroup)
             @subgroup = ();
             save current sequence number as last
             save the current data of interest
             next
[download]

For summarize(@subgroup), I don't quite get from your question what the processing you do is (record first and last in group and sum fields?). Anyway - your gap finding is missing, and you need to add logic for the two different kinds of gaps before you can summarize.