UPDATE: I
FINALLY got this to work!!! I finally was able to figure out how to turn off the grayed-out "Repeat header rows"!!! I placed my cursor anywhere inside the table, then went to Table Tools / the Layout tab. Far over on the right side
of the Layout ribbon, I found "Repeat Header Rows" and it was selected / turned on. Once I unselected that, the table (very long box of text that flows across almost 3 pages) is now working perfectly.....breaking where it needs to break, etc. I appreciate
all the information above....I tried just about everything that was suggested!
When you enable the "Repeat header rows" option it applies to the selected rows, and you can't turn it off for the first row and leave it selected for the rest of the rows, as you have noticed.
As I wrote in August 2016, it would be better if Word prevented you from selecting the option in such a way that it doesn't function properly.