If your data is delimited by a blank line then you can change the $/ (input record seperator) variable to read in chunks of the file up to every double newline. Something like this should get you started on parsing your file

{
  local $/ = "\n\n";
  while(<INPUT1>) {
    my($head,$data) = m< ^ \* ([^\n]+) \n (.*?) $/ >xm;
    push @seqs    => [ split /\n/, $data ];
    push @headers => $head;

    print OUTFILE  "$head\n";
    print OUTFILE2 @{ $seqs[-1] }, "\n";
  }
}
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The above code should save the data into @seqs which will be an array of arrasy, and the headers into @headers as a simple array, all the while printing the data into OUTFILE2 and the headers into OUTFILE. A couple of errors in your code were that you were exitting in the case of the first condition (maybe you meant next?) and you forgot to escape * in the second condition, which should've triggered a compile-time error.
HTH

_________
broquaint