Algorithmically golfed: (golfed without employing space-saving techniques, otherwise it would look scary :P)

open (OLD, "<$old_file.txt") || die $!;
my $i;
foreach (split (/====\s*\n(?=\d+)/, do{local$/;<OLD>}))
{
    open (NEW,">$old_file$i.txt") || die $!;
    print NEW $_;
    close (NEW);
    $i++;
}
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