Instead of counting rows, nest tables.
Create an outer table that's 1 cell only and set it up so that it doesn't change size but don't set it up to disallow wrapping the row to the next page. This table should encompass the area where you want your real table to be. Of course, disable the outer table's borders if you want it hidden.
Inside the outer table, define your real table. Set this up as you would.
Because the outer table is fixed, when the real table fills it up, it will spill over the next page (because you allowed wrapping).
When nesting tables, make sure you place an "empty" field in the cell before you define your inner table - a field that has <?if:1=0?><?end if?>. BIP won't render that field because the condition won't be true. BTW, that is how I place comments in the template. Placing an empty field will ensure that Word doesn't combine the object handles of the outer and inner tables.