Nibbling regex are expensive. Change it to a scalar m/\G.../g walk, and you have a winner:

use strict;
my $line;
while ($line = <DATA>) {
  chomp $line;
  print $line,"\n";
  while ($line =~ m/\G(?:([^" ]+)|"([^"]+)")(?: |$)/g) {
    print ">>>",$1||$2,"\n";
    print $line,"\n";
  };
};
__DATA__
"72 3267S" "S2079" 1 no
"72 0250" "S3011" 1 no
"72 8351S" "S6101" 1 no
"72 17082S" "S6108" 1 no
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-- Randal L. Schwartz, Perl hacker