If you have the merge fields inserted into the cells of a one row table, via
the Table Properties dialog, uncheck the "Allow row to break across pages"
attribute.

It that attribute does not get carried over to the document produced by
executing the merge, select the whole table in that document and set that
attribute for it.

Another thing that you could try if you have multiple paragraphs in the mail
merge main document, it to select all but the last of them and set the
attribute for the selected paragraphs to Keep with Next in the Format
Paragraph dialog, and select all of the paragraphs and set the Keep (lines)
together attribute.