I am not fully understanding the question.
AFAIK, Word can never end with a table. It always has a real paragraph mark as the terminating character. In other words, if you go to the end of a document, insert a table, Word will add a paragraph mark after the table.
However, what I am not following is: "Any rows below it are not recognized as part of the table. "
What rows? If they are rows, I have to assume they are in a real table. In which case, if you want that table to be part of the previous table, just do what macropod suggested. Delete the intermediate paragraph mark. The following table will - or should - merge with the preceding one.
Gerry