Here is an explanation of why your code works the way it does and how to make it do what you want (with minimal changes). Your 1st substitution attempt (pos1) is successful, as you've noted. So, you've replaced the 10th | with "pipe". Now, you again want to replace the 10th | with "pipe", not the 11th:

use warnings;
use strict;

while (my $row = <DATA>) {
    my $pos1 = 10;
    $row =~ s/(\|)/!--$pos1 ? ' pipe ' : $1/ge;
    my $pos2 = 10;
    $row =~ s/(\|)/!--$pos2 ? ' pipe ' : $1/ge;
    my $pos3 = 10;
    $row =~ s/(\|)/!--$pos3 ? ' pipe ' : $1/ge;
    chomp $row;
    print "$row\n";
}
print "doneagain\n";

__DATA__
1|2|3|4|5|6|7|8|9|a|b|c|d|e|f|g|h|i
[download]

Outputs:

1|2|3|4|5|6|7|8|9|a pipe b pipe c pipe d|e|f|g|h|i
doneagain
[download]