Bootstrap Tabs Maintain Selected (Active) Tab on Partial PostBack inside AJAX UpdatePanel in ASP.Net

You need to call the same code after AJAX UpdatePanel Partial PostBack is completed.

 Reference: Call JavaScript function after AJAX UpdatePanel Refresh (Partial PostBack) in ASP.Net

<asp:ScriptManager ID="ScriptManager1" runat="server">
</asp:ScriptManager>
<asp:UpdatePanel ID="UpdatePanel1" runat="server">
    <ContentTemplate>
        <link rel="stylesheet" href="http://maxcdn.bootstrapcdn.com/bootstrap/3.3.2/css/bootstrap.min.css" />
        <script type="text/javascript" src="http://ajax.googleapis.com/ajax/libs/jquery/1.9.1/jquery.min.js"></script>
        <script type="text/javascript" src="http://maxcdn.bootstrapcdn.com/bootstrap/3.3.2/js/bootstrap.min.js"></script>
        <div class="panel panel-default" style="width: 500px; padding: 10px; margin: 10px">
            <div id="Tabs" role="tabpanel">
                <!-- Nav tabs -->
                <ul class="nav nav-tabs" role="tablist">
                    <li><a href="#personal" aria-controls="personal" role="tab" data-toggle="tab">Personal
                    </a></li>
                    <li><a href="#employment" aria-controls="employment" role="tab" data-toggle="tab">Employment</a></li>
                </ul>
                <!-- Tab panes -->
                <div class="tab-content" style="padding-top: 20px">
                    <div role="tabpanel" class="tab-pane active" id="personal">
                        This is Personal Information Tab
                    </div>
                    <div role="tabpanel" class="tab-pane" id="employment">
                        This is Employment Information Tab
                    </div>
                </div>
            </div>
            <br />
            <br />
            <asp:Button ID="Button1" Text="Submit" runat="server" CssClass="btn btn-primary" />
            <asp:HiddenField ID="TabName" runat="server" />
        </div>
    </ContentTemplate>
</asp:UpdatePanel>
<script type="text/javascript">
    $(function () {
        SetTabs();
    });
    var prm = Sys.WebForms.PageRequestManager.getInstance();
    if (prm != null) {
        prm.add_endRequest(function (sender, e) {
            if (sender._postBackSettings.panelsToUpdate != null) {
                SetTabs();
            }
        });
    };
    function SetTabs() {
        var tabName = $("[id*=TabName]").val() != "" ? $("[id*=TabName]").val() : "personal";
        $('#Tabs a[href="#' + tabName + '"]').tab('show');
        $("#Tabs a").click(function () {
            $("[id*=TabName]").val($(this).attr("href").replace("#", ""));
        });
    };
</script>
</form>