Resolution
for [Update panel button not working in web part.]
Replace your <body> content with below content with in SharePoint 2013 master page
------------------------------------------------------------------------------------------------------------
Master Page issue
<body>
<SharePoint:ImageLink runat="server" />
<SharePoint:SPNoScript runat="server" />
<SharePoint:SPClientIDGenerator runat="server" ServerControlID="DeltaPlaceHolderMain;DeltaPlaceHolderPageTitleInTitleArea;DeltaPlaceHolderUtilityContent" />
<SharePoint:SharePointForm runat="server" onsubmit="if
(typeof(_spFormOnSubmitWrapper) != 'undefined') {return
_spFormOnSubmitWrapper();} else {return true;}">
<script type="text/javascript"> var submitHook = function () { return false; }; theForm._spOldSubmit = theForm.submit; theForm.submit
= function
() { if
(!submitHook()) { this._spOldSubmit(); } }; </script>
<SharePoint:AjaxDelta ID="DeltaSPWebPartManager" runat="server">
<WebPartPages:SPWebPartManager runat="Server" />
</SharePoint:AjaxDelta>
<asp:ScriptManager ID="ScriptManager" runat="server" EnablePageMethods="false" EnablePartialRendering="true" EnableScriptGlobalization="false" EnableScriptLocalization="true" />
<SharePoint:AjaxDelta ID="DeltaDelegateControls" runat="server">
<SharePoint:DelegateControl runat="server" ControlId="GlobalNavigation" />
<SharePoint:DelegateControl ControlId="GlobalSiteLink3" Scope="Farm" runat="server" Visible="false" />
</SharePoint:AjaxDelta>
<SharePoint:AjaxDelta ID="DeltaPlaceHolderPageTitleInTitleArea" runat="server">
<asp:ContentPlaceHolder ID="PlaceHolderPageTitleInTitleArea" runat="server">
</asp:ContentPlaceHolder>
</SharePoint:AjaxDelta>
<div id="sideNavBox" class="ms-dialogHidden
ms-forceWrap ms-noList">
<div class="ms-core-navigation">
<SharePoint:AjaxDelta ID="DeltaPlaceHolderLeftNavBar" BlockElement="true" CssClass="ms-core-navigation" role="navigation" runat="server">
<asp:ContentPlaceHolder ID="PlaceHolderLeftNavBar" runat="server">
<asp:ContentPlaceHolder ID="PlaceHolderLeftNavBarTop" Visible="false" runat="server">
</asp:ContentPlaceHolder>
<asp:ContentPlaceHolder ID="PlaceHolderQuickLaunchTop" Visible="false" runat="server" />
<asp:ContentPlaceHolder ID="PlaceHolderLeftNavBarDataSource" Visible="false" runat="server" />
<asp:ContentPlaceHolder ID="PlaceHolderCalendarNavigator" Visible="false" runat="server" />
<asp:ContentPlaceHolder ID="PlaceHolderLeftActions" Visible="false" runat="server" />
<asp:ContentPlaceHolder ID="PlaceHolderQuickLaunchBottom" Visible="false" runat="server" />
</asp:ContentPlaceHolder>
</SharePoint:AjaxDelta>
</div>
</div>
<div id="TurnOnAccessibility" style="display: none" class="s4-notdlg
noindex">
<a id="linkTurnOnAcc" href="#" class="ms-accessible ms-acc-button" onclick="SetIsAccessibilityFeatureEnabled(true);UpdateAccessibilityUI();document.getElementById('linkTurnOffAcc').focus();return
false;">
<SharePoint:EncodedLiteral runat="server" Text="<%$Resources:wss,master_turnonaccessibility%>" EncodeMethod="HtmlEncode" /></a>
</div>
<div id="TurnOffAccessibility" style="display: none" class="s4-notdlg noindex">
<a id="linkTurnOffAcc" href="#" class="ms-accessible ms-acc-button" onclick="SetIsAccessibilityFeatureEnabled(false);UpdateAccessibilityUI();document.getElementById('linkTurnOnAcc').focus();return
false;">
<SharePoint:EncodedLiteral runat="server" Text="<%$Resources:wss,master_turnoffaccessibility%>" EncodeMethod="HtmlEncode" /></a>
</div>
