Hello,
this appears to be a bug - the undeletable aspect should still be present when the node is transferred to the archive. This may have something to do how the SiteService supresses the behavior - this also supresses the copy of the aspect, which then leads to an inconsistent state in the archive as the aspect is configured as being mandatory.
You should be able to reconstruct your site after a JavaScript-based modification while it is still in archive. Write and execute a script action that re-adds the aspect on the site node before trying to recover it.
Regards
Axel