The context of the click event handler (the object that this refers to in that handler) is not propagated to your AJAX success callback.
You can capture the value of this from the caller by assign it to a local variable, or you can explicitly propagate it by passing this in the context option to $.ajax():
$.ajax({
url: window.config.AJAX_REQUEST,
type: "POST",
data: {
action: "DELCOMMENT",
comment: $("#commentText").val(),
comment_id: $(this).attr("href")
},
context: this,
success: function(result) {
$(this).fadeOut("slow"); // Works, since 'this' was propagated here.
}
});