If you run the following javascript on the page you will enable partial rendering for all of the modules that support it.

$("div[id$='View_UP']").each(function() {
        if (!($(this).parent().attr('id').indexOf("View_UPPanel") >= 0)) {
            var prefix = $(this).attr("id").replace("View_UP", "");
            $(this).wrap("<div id='" + prefix + prefix + "View_UPPanel' />");
        }
    });

At least, it worked for me.

As I evaluated the DOM I noticed that only the module that wrapped the div with the id of "*View_UP" in a div with an id of "*View_UPPanel" actually worked correctly.  This script makes sure that all of the "*View_UP" panels are wrapped.

Sorry, I've been meaning to post and update to this for a few days now.  Here's the new(er) code.

    // because the separator could be an underscore or a dollar sign (or who knows what else)
    var viewUpId = $("div[id$='View_UPPanel']").attr("id");
    viewUpId = viewUpId.replace("View_UPPanel", "");
    var token = viewUpId.charAt(viewUpId.length - 1);
    // correct partial postback bug in dnn.
    $("div[id$='View_UP']").each(function () {
        if (!($(this).parent().attr('id').indexOf("View_UPPanel") >= 0)) {
            var prefix = $(this).attr("id").replace("View_UP", "");
            $(this).wrap("<div id='" + prefix + prefix.replace(/_/g, token) + "View_UPPanel' />");
        }
    });

The problem, as noted in the comment, is that on my dev machine they were using an underscore and on the stage computer they were using a dollar sign to separate the concatenation. The above code detects which they are using and then applies that code similar to what I provided before.

This is all part of
$(function ($) {
   // code goes here.
});

and does not need to be added to
Sys.WebForms.PageRequestManager.getInstance().add_endRequest

 since the part of the DOM we are modifying will never change due to partial rendering.