If the blog setting Index display: is set to Group posts monthly navigation buttons « Previous month and Next month » will be displayed.

It doesn't make sense to have a button « Previous month (or at least it should be disabled) if we reach the first blog post ever published. In a same way it doesn't make sense to display Next month » button if we reach the latest blog post published (or latest draft for a user who have edit privilege).

The issue related to keeping those links can arise if a crawler (or a link checker) try to index pages following the links on those buttons: it will end up in an infinite loop.

The same situation probably happen with Group posts weekly.