org-export-with-archived-trees

org-export-with-archived-trees is a variable defined in `ox.el'.
Its value is

headline

Documentation:
Whether sub-trees with the ARCHIVE tag should be exported.

This can have three different values:
nil Do not export, pretend this tree is not present.
t Do export the entire tree.
`headline' Only export the headline, but skip the tree below it.

This option can also be set with the OPTIONS keyword,
e.g. "arch:nil".

You can customize this variable.