I had this issue where I wanted more than one row of headers in the TabContainer as I had a large number of panels and was not able to fit them in the page.
Here is the solution. [make sure you download the toolkit with source]
Open the AJAX Control Toolkit's solution by clicking on the solution file inside the toolkit folder.
Open the file Tabs.css under AjaxControlToolkit/Tabs/Tabs.css
And make the following changes.
/* default layout */.ajax__tab_default .ajax__tab_header {}
.ajax__tab_default .ajax__tab_outer {display:-moz-inline-box;display:inline-block}
.ajax__tab_default .ajax__tab_inner {display:-moz-inline-box;display:inline-block}
.ajax__tab_default .ajax__tab_tab {margin-right:4px;overflow:hidden;text-align:center;cursor:pointer;display:-moz-inline-box;display:inline-block}
Now click on Build -> Build Solution to build the solution.
Use the AjaxControlToolkit.dll under ToolkitTests/Bin folder as your reference from now on.
Add this dll file as reference to your current website and you should have the 2 rows.