It appears that the more heavily customized your existing template is, the more likely you will run into archiving problems.
Here is one cure: overwrite the archive line in your template with some stock archive language from one of the new Blogger templates. For example:
[$BlogItemAuthorNickname$] @ [a href="[$BlogItemPermalinkUrl$]" title="permanent link"][$BlogItemDateTime$][/a]
For this example, angle brackets (< and >) were replaced by square brackets ([ and ]) to get the line to display rather than execute. You would need to replace the square brackets with angle brackets.
Highlight your existing archive line and put this in its place EVEN IF THEY LOOK THE SAME.
This was the only thing that solved out double-link problem that caused a 404 error whenever anyone tried to use an archive link. It now seems to be working.