[Fixed]-Ajax function doesn't execute when any of the input fields are not supplied in django

It sounds like those values are optional?

If so, perhaps you can check to see if those values exist, and if not, just submit an empty string:

data: {
                'pname_Aj': ( $('#pname').val() || ""),
                'psection_Aj': ( $('#psection').val() || ""),
                'rinput_Aj' : (JSON.stringify(fun()) || ""),
                'csrfmiddlewaretoken':$("input[name=csrfmiddlewaretoken]").val()
            },

So if the user has entered values in those sections (and fun() returns something that can be stringified, those variables get submitted. Otherwise, an empty string gets submitted.

If the parameters need to be absent when no value

function saveprof() {
    $('.spinner').show();
    $.ajax({
        type: "POST",
        url: "saveprof",
        enctype: 'multipart/form-data',
        async: true,
        data : function() {
            var data = {};
            var addToData = function(name, val) {
                if(val) {
                    data[name] = val;
                }
            }
            addToData('pname_Aj', $('#pname').val());
            addToData('psection_Aj', $('#psection').val());
            addToData('rinput_Aj', JSON.stringify(fun()));
            addToData('csrfmiddlewaretoken', $("input[name=csrfmiddlewaretoken]").val());
            return data;
        }(),
        success: function (data, textStatus, jqXHR) {
            $('#message').html(data);
            window.location.href = 'myprofile';
            window.location('myprofile');  
            $('.spinner').fadeOut();
        }
    });
}