I am only interested in the length of the longest

In that case, this should work. Nothing special, but just one pass of the string:

#! perl -slw
use strict;

sub z {
    my $soFar = 1;
    my $lastC = substr $_[0], 0, 1;
    my $lastS = $lastC <=> substr $_[0], 1, 1;
    my $bestN =  0;

    for my $p ( 1 .. length( $_[0] )-1 ) {
        my $this = substr $_[0], $p, 1;
        my $d = abs( $this - $lastC );
        my $s = $this <=> $lastC;
        $s *= -1 if $d == 9;

        if( $s != $lastS or $d != 1 and $d != 9 ) {
            $soFar = 1;
            $lastS = $s;
        }
        if( ++$soFar > $bestN ) {
            $bestN = $soFar;
        }
        $lastC = $this;
    }
    return $bestN;
}

while( <DATA> ) {
    chomp;
    my $l = z( $_ );
    print $_, ' : ', $l;
}

__DATA__
01234567890987654321
01234567890123456789
78901234567890123456
98765432109876543210
21098765432109876543
012345678890123456789
789012345677890123456
987654321099876543210
210987654322109876543
012345678900987654321
[download]

That is one nasty, messy problem :)