ASPxTreeList does not save a focused node in cookies. However, you can add this capability by saving and restoring a focused node to cookies manually:
[JScript]function OnFocusedNodeChanged(s, e){ ASPxClientUtils.SetCookie(s.name + '_focudedKey', s.GetFocusedNodeKey());}function OnInit(s, e){if(ASPxClientUtils.GetCookie(s.name+'_focudedKey')!=null) s.SetFocusedNodeKey(ASPxClientUtils.GetCookie(s.name+'_focudedKey'));}