No, you *don't* have to insert a section break to get a new header. If the
table is just three pages long, insert a section break before the table.
Format the section as "Different first page." Put the header for the first
page of the table in the First Page Header of that section. Put the header
for the subsequent pages in the Header. If you need a different header for
every page of the table, then check "Different odd and even" as well and use
the Even Page Header and Odd Page Header. Be aware, however, that "Different
odd and even" will apply to the entire document ("Different first page" can
be enabled for a single section or specific sections).

There is no way to make a heading row repeat over a section break; there
*is*, however, as I pointed out, a way to make them repeat over a page
break.