It turn out that the solution here is very simple. When you add a table to a form, there is no border around the cells. It looks like there is when you're filling out the form because the fields are all input fields, but in reality--no borders. When the form is submitted to the repository, the input fields become span elements, and borders aren't added. If you want a border, consider styling your table using CSS. To do this, add a CSS class to your table. Almost anything will do; when I tested this out, I used "test", but I recommend using something more descriptive. To add borders around the cells, I used one simple line of CSS:

.test td {border: 1px solid;}

Now, of course, you'll want to play with the CSS to make your table look the way you want it to. The important thing is that the styling will be included on the submitted form. 

If you'd like more information about CSS styling for tables, take a look at this MDN article. It should help get you started.