REPRO

    Run the snippet below
    Inspect the DOM (at the beginning of the form you will see the .rtbSlide element)
    Click the toolbar button to invoke an ajax request

actual: the .rtbSlide element is multiplied with every request

expected: the toolbar is fully disposed

        <asp:UpdatePanel runat="server">
            <ContentTemplate>
                <telerik:RadToolBar RenderMode="Lightweight" ID="RadToolBar1" runat="server"
                    AutoPostBack="true">
                    <Items>
                        <telerik:RadToolBarButton Text="postback to test">
                        </telerik:RadToolBarButton>
                    </Items>
                </telerik:RadToolBar>
            </ContentTemplate>
        </asp:UpdatePanel>


WORKAROUND

        <script>
            var oldDispose = Telerik.Web.UI.RadToolBar.prototype.dispose;
            Telerik.Web.UI.RadToolBar.prototype.dispose = function()
            {
                if (this._moreButtonDropDown && typeof this._moreButtonDropDown.dispose == 'function') {
                    this._moreButtonDropDown.dispose();
                }
                oldDispose.call(this);
            }
        </script>

The click event of the toolbar is triggered only when the user clicks outside of the set button icon (the text or the button element). Clicking directly over the icon does not perform any action in IE11.

video: https://www.screencast.com/t/K50K4X8Ck

Code to reproduce:
            <telerik:RadToolBar runat="server" ID="ToolBar1">
                <Items>
                    <telerik:RadToolBarButton
                        ImageUrl="//d585tldpucybw.cloudfront.net/sfimages/default-source/labs/kendo/kendoka-states.png"
                        NavigateUrl="Default.aspx"
                        Text="Link"/>
                    <telerik:RadToolBarButton
                        ImageUrl="//d585tldpucybw.cloudfront.net/sfimages/default-source/labs/kendo/kendoka-states.png"
                        NavigateUrl="Default.aspx"/>
                </Items>
            </telerik:RadToolBar>

When an item with controls in the item template is collapsed, the AJAX settings are broken as the control's DOM element is moved because the MoreButton dropdown is not part of the Toolbar element itself. 

The solution is to set the overflow property of the item to Never - <telerik:RadToolBarButton OverFlow="Never"> 
https://docs.telerik.com/devtools/aspnet-ajax/controls/toolbar/mobile-support/responsive-design#preventing-items-from-being-collapsed