"allow row to break across pages" doesn't work in my MS word 2013
This was my problem too. The problem may be that every row in the table had the attribute "Heading Rows Repeat". To resolve, select the entire table. In 'Table Properties...', on the "Row" tab, uncheck "Repeat as header row at the top of each page". Then highlight only the top row and recheck if you do want the header row to repeat (which I always recommend.) That should do.
It appears to be a bug in WD2013. Workaround: try to UNCHECK "Repeat as header row at the top of each page."
To keep all the rows on a single page:
- Select the entire table
- Select Paragraph Settings -> Keep with next
I always thought it was under Table properties/Row/do not allow row to break across pages, but this setting actually only applies to a single row with multiples lines breaking across a page.