It seems to work for me:

use warnings;
use strict;

while (<DATA>) {
    my $pat = $_;
    $pat =~ s/_x_x$//i;   #This is not working.
    $pat =~ s/_x_s$//i;   #This is working.
    $pat =~ s/_x$//i;     #This is not working.
    print $pat;
}

__DATA__
foo_x_x
boo_x_s
moo_x
[download]

Prints:

foo
boo
moo
[download]

What does $pat have before s///? See also:

• Basic debugging checklist