I created a template, used it to create an article, and published the article.

Then I realized I needed another section at the beginning of articles like
this, so I changed the template to include the new first section (keeping all
the other sections).

I unpublished the article, edited it to include appropriate content under
the new first section, and saved it.

Instead of the new content being saved under the first heading, it was saved
under the second heading, and all the content in each subsequent heading was
bumped down one. The content from the last section was lost.

When I tried again, everything got bumped down again, and another section's
content was bumped out of existence.

No workaround that I could find - just don't add sections to templates that
are in use. Something got out of sync, apparently. I did not test this by
adding new sections in other positions (than first), or at the end.