I think I have solved the problem.

When I add a new table to my document, I often copy the top row of another table, and then Insert rows below it to build it up. This seems to be what causes Word to separate the table from the row above it.

I have found if I create a new table by copying an entire table, and using that as a template for a new table, then Word keeps the table and the blank row above it all together.

Thanks for your help.