Você está se superando com o uso de shift
:
while [ $# -gt 0 ] ; do
case "$1" in
-f|--file)
f="$2" # Re-ordered for consistency
shift
;;
-s|--string)
s="$2"
shift
;;
-c|--client)
c="$2" # this was $3, which was the error
shift
;;
-h|-help)
_usage
;;
-*)
_usage
;;
esac
shift
done