In Sphinx-1.3.5, the counter of tables is overrided by code-block's in latex output.
You can see the caption of table starts with 'Listings ...' in following screenshot:

The screenshot above is generated from following reST:

.. list-table:: hello-table
   :header-rows: 1

   * - Hello
     - World
   * - Hello
     - World

.. code-block:: python
   :caption: hello-world

   print('Hello world')

.. code-block:: python
   :caption: hello-world

   print('Hello world')

.. list-table:: hello-table
   :header-rows: 1

   * - Hello
     - World
   * - Hello
     - World

This behavior comes from the combination of threeparttable and captionof.
As a test, I wraped the threeparttable in table environment. Then the problem was fixed.