The issue is observable when AJAX is enabled using asp:UpdatePanel, telerik:RadAjaxPanel, or telerik:RadAjaxManager because the event handlers are not added back to elements upon an AJAX postback. When no AJAX panels are used, the entire document is rendered, and all handlers are attached to elements again.
Code
<asp:UpdatePanel runat="server">
<ContentTemplate>
<telerik:RadAutoCompleteBox ID="RadAutoCompleteBox1" runat="server"></telerik:RadAutoCompleteBox>
<asp:Button ID="Button1" runat="server" Text="Post Back" />
</ContentTemplate>
</asp:UpdatePanel>
<script>
$(document).on('click', function (e) {
console.log('Document clicked');
});
</script>