Try alerting the value you are submiting to see if it's ok.
I also suggest that you use your browser Network Profiler (in development tools) to analyse if the request is being made, and if so what's is being sent and what's being recieved.
var valToEdit = edit_form.user_edit.value;
alert("Editing: " + valToEdit);
$.post(
'edit_script.php',
{user_edit: valToEdit},
function (dresult, textStatus) {
alert("Result: " + textStatus);
$("#d_result").html(dresult).show();
}
);
If this doesn't help, try swting to .ajax()
and use an error callback function.