Problems

When I select a row from the GridView on "TabPanel2", the ActiveTabIndex is not maintained and appears to be reset.

ASPX 

<%@ page autoeventwireup="true" codefile="Tabs.aspx.cs" inherits="Tabs" language="C#"
	title="Untitled Page" %>

<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">
<html xmlns="http://www.w3.org/1999/xhtml">
<head id="Head1" runat="server">
	<title>Untitled Page</title>
</head>
<body>
	<form id="form1" runat="server">
		<aspx:scriptmanager id="ScriptManager1" runat="server">
		</aspx:scriptmanager>
		<ajax:tabcontainer id="TabContainer1" runat="server">
			<ajax:tabpanel id="TabPanel1" runat="server" headertext="TabPanel1">
				<contenttemplate>
				TabPanel1
				</contenttemplate>
			</ajax:tabpanel>
			<ajax:tabpanel id="TabPanel2" runat="server" headertext="TabPanel2">
				<contenttemplate>
				TabPanel2
				<asp:gridview id="GridView1" runat="server" autogenerateselectbutton="true">
				</asp:gridview>
				</contenttemplate>
			</ajax:tabpanel>
		</ajax:tabcontainer>
	</form>
</body>
</html>

CODE-BEHIND 

using System;
using System.Collections.Generic;

public partial class Tabs : System.Web.UI.Page
{
    protected void Page_Load(object sender, EventArgs e)
    {
		if (!this.IsPostBack)
		{
			List<int> numbers = new List<int>();

			for (int i = 1; i < 11; i++)
			{
				numbers.Add(i);
			}

			GridView1.DataSource = numbers;
			GridView1.DataBind();
		}
    }
}
 

Solutions

I looked into it. It seems it's caused by not saving client state correctly when the postback is triggered by GridView. My solution is saving it manually.

<%@ Page Language="C#" %>

<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">

<script runat="server">

    protected void Page_Load(object sender, EventArgs e)
    {
        if (!this.IsPostBack)
        {
            System.Collections.Generic.List<int> numbers = new System.Collections.Generic.List<int>();

            for (int i = 1; i < 11; i++)
            {
                numbers.Add(i);
            }

            GridView1.DataSource = numbers;
            GridView1.DataBind();
        }
    }
</script>

<html xmlns="http://www.w3.org/1999/xhtml">
<head id="Head1" runat="server">
	<title>Untitled Page</title>
	<script type="text/javascript">
	function OnChanged(sender, args)
	{
	    sender.get_clientStateField().value = sender.saveClientState();
	}
	</script>
</head>
<body>
	<form id="form1" runat="server">
		<asp:scriptmanager id="ScriptManager1" runat="server">
		</asp:scriptmanager>
		<ajaxtoolkit:tabcontainer OnClientActiveTabChanged="OnChanged" id="TabContainer1" runat="server" ActiveTabIndex="0">
			<ajaxtoolkit:tabpanel id="TabPanel1" runat="server" headertext="TabPanel1">
				<contenttemplate>
				TabPanel1
				</contenttemplate>
			</ajaxtoolkit:tabpanel>
			<ajaxtoolkit:tabpanel id="TabPanel2" runat="server" headertext="TabPanel2">
				<contenttemplate>
				TabPanel2<asp:Button ID="Button1" runat="server" Text="Button" />
				<asp:gridview id="GridView1" runat="server" autogenerateselectbutton="True">
				</asp:gridview>				
				</contenttemplate>
			</ajaxtoolkit:tabpanel>
		</ajaxtoolkit:tabcontainer>
	</form>
</body>
</html>