I couldn't find any official way of doing this through the Telerik APIs, nor any useful advice on their forum, so I decided to go it my own way with the use of:
- Html.Telerik().TabStrip().ClientEvents() both the OnSelect() and OnLoad()
- The cookie plugin for jQuery 
Then I wired them up as below, in the partial view that contains the TabStrip.
.ClientEvents(events => events
.OnSelect(() =>
{ 
    %>
    function(e) {
        var item = $(e.item);
        $.cookie('selectedTabIndex', item.index(), { path: '/' });
    }
    <%
})
.OnLoad(() =>
{ 
    %>
    function(e) {
        var tabStrip = $("#TabStrip").data("tTabStrip");
        var index = $.cookie('selectedTabIndex');
        var domElement = $("li", tabStrip.element)[index];
        tabStrip.select(domElement);
    }
    <%
})
)
Edit: I realised that my answer was little bit lacking in explanation so I've added:
  In case it's not obvious, the OnSelect
  is capturing the index of the selected
  tab when it is selected and writing
  that to a cookie called
  selectedTabIndex. The path is being
  set so it will cover our whole site,
  but if you leave that out it will
  create a new cookie for each different
  path (which may be your desired
  behaviour). Someone more familiar with
  the jQuery cookie plugin please
  correct me if I'm wrong there, I
  haven't used it much.
  
  Then in the OnLoad it's doing the
  opposite, basically. It finds the
  tabStrip, gets the index from the
  cookie, then gets the domElement of
  the tab at the index from the cookie
  and tells the tabStrip to select that
  domElement.
This seems to work pretty well in Chrome and IE, but there may be some quirks in FFox 3.
I hope the Telerik team considers adding this to their API, as it strikes me as being a pretty useful feature to have baked-in. Apologies if it already is, but I couldn't find it in the docs.