Damn! The "simplifications" I applied subtly changed the results. Please try again with the original version I posted and see if that matches your existing method?

sub rankSums {
    my( $aRef, $bRef ) = @_;
    my( $aSum, $bSum ) = (0) x 2;
    my( $a, $b ) = (0) x 2;
    my $rank = 1;
    while( $a < @$aRef && $b < @$bRef ) {

        if( $aRef->[ $a ] < $bRef->[ $b ] ) {
            $aSum += $rank++;
            ++$a;
        }
        elsif( $aRef->[ $a ] > $bRef->[ $b ] ) {
            $bSum += $rank++;
            ++$b
        }
        else {
            my $d = 2;
            my( $aSaved, $bSaved ) = ( $a, $b );
            ++$d, ++$a while $a < $#{ $aRef } && $aRef->[ $a ] == $aRe
+f->[ $a + 1 ];
            ++$d, ++$b while $b < $#{ $bRef } && $bRef->[ $b ] == $bRe
+f->[ $b + 1 ];
            my $s = sum( $rank .. $rank + $d - 1 ) / $d;
            $aSum += $s * ( $a - $aSaved + 1 );
            $bSum += $s * ( $b - $bSaved + 1 );
            $rank += $d;
            ++$a, ++$b;
        }
    }
    $aSum += $rank++ while $a++ < @{ $aRef };
    $bSum += $rank++ while $b++ < @{ $bRef };

    return $aSum, $bSum;
}
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The bonus is (assuming it's correct this time), is that with datasets containing many ties, it actually runs faster too.