Microsoft Word is skipping table caption numbers - how to debug?

Method 1: Update Field

1. Highlight entire document: Ctrl-A
2. Right click on any table caption number (highlighted in a darker grey)
3. Click "Update Field"

Method 2: Insert temporary table

1. Insert a new table at the end of the document.
2. Add a caption, with numbering. (All previous numbers should update.)
3. Remove the new table.

I created five tables and put a table caption on each. I removed the first table and the remaining tables did not update. Either method above will renumber the tables appropriately.

Manually restart numbering:

Ensure no traces of the "missing" table exist by highlighting and deleting all content between the tables with a missing number. Then perform either method above. If there is still a gap in the numbering, try overriding the numbering.

1. Right-click the first incorrect field number.
2. Click "Edit Field"
3. Click "Options" (button)
4. Select "Field Specific Switches" (tab)
5. Select "\r" and click "Add to Field" button
6. Type the new field code number (in your case: 2) into the Field Codes textbox
7. Click OK twice
8. Update all fields using either method above.

There was a hidden empty caption box in some white space on the page. after I deleted it the numbering was restored. I found this through clicking, by chance, on that white space.

1. You should probably start by making a backup copy of your document (or make a working copy, in which to do the following).
2. Press Alt+F9 to reveal all field codes.
3. Click on "Home" → "Editing" → "Find" → "Go To", or press Ctrl+G, to open the "Find and Replace" dialog box, "Go To" tab.  In the "Go to what" box, select "Field".  Click "Next". 
4. Then click "Next" repeatedly, or close the dialog box and press Ctrl+PgDn repeatedly, to step through all the fields in the document.  These will include all the figure/table/equation numbers, any cross-references, and probably some other things.
5. Be on the lookout for field codes where you wouldn't expect one to be.  If you find any, investigate them, and delete them unless you can justify why they exist.