And why would you slurp-and-split instead of processing the file sequentially? Something along the lines of:

my $c_para = '';
while (<$INPUT_FH>) {
   $c_para.=$_;

   if ( /$end_of_para_pattern/ ) {
     process_paragraph($c_para);
     $c_para = '';  # we'll start a new paragraph next pass
   }

}
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has always worked for me. If you really needed an array of paragraphs, you could always push them onto an array instead of calling process_paragraph...