I recently came across an issue where JQuery bindings no longer functioned after a partial postback and stumbled upon some code that was helpful in most cases.

Javascript (JQuery):

Sys.Application.add_load(startJQuery); 

startJQuery() { 
//do JQ here
}

And alternatively..

Sys.WebForms.PageRequestManager.getInstance().add_endRequest(function(){});

This code will not always work however, as was the case in my particular scenario, so I resolved using an alternate method.

RegisterStartupScript is great functionality, and can be useful for loading javascript dynamically on an as-needed basis.

The example below, based on prior code selects the correct JS file to use, then loads it using the registerstartupscript function. This is all within a code block which calls an update panel

C#:

int scriptnumber = 1;
string FilePath = String.Format("~/Scripts/Script_{0}.js",scriptnumber.ToString());
System.IO.StreamReader sr = new System.IO.StreamReader(HttpContext.Current.Server.MapPath(FilePath));
            jqueryfileoutput = sr.ReadToEnd();

            upnlBodyContent.Update();

            ScriptManager.RegisterStartupScript(this, this.GetType(), "scriptname",
                "<script type=\"text/javascript\">" + jqueryfileoutput.ToString().Trim() + "</script>", false);