We have solved the problem. The cause seems most likely to have been Retrospect's new automatic client update feature. In any case, at some point the client software on the affected machines became corrupted or was actually deleted. In the cases we tested, if the client was removed from the sources list and we attempted to re-add it, the process failed due to an incorrect public/private keypair. We decided to just go ahead and reinstall the client software locally on all our "invisible" Windows clients, which solved the problem; we did not need to delete any client configuration files, so these must have been OK.