[Edit: See second and fourth messages below for bottom line.]

Information that would help:
Version of Word? There are bunches in use, with somewhat different quirks.
Method of saving as pdf? (There are at least three).

Word treats headings inside tables as being different for many purposes. This may be the source of your problem, or not. I can confirm that it is a problem with Word 2013 and earlier.

Simplest solution may be to move the headings outside the tables.

See also Why use Microsoft Word’s built-in heading styles? by Shauna Kelly and When Headings Aren't Really Headings.

Are you sure that when you copy into the table that you are bringing along the paragraph style? Especially with linked styles this can be a problem. It looks the same and will have the same style name but not be the same.