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Imagine I'm setting up a blog to document the expired cans of food in my kitchen.
My front page is a traditional blog, displaying my latest posts in chronological order.
My sidebar has links sorting posts by categories such as, "Expires today," "Expires next week," and so on. When a post expires, it gets removed from that category, but the post is not deleted.
Another set of category links sort posts by such things as, "Soups," "Vegetables," and "Beans." Again, expired posts get removed from those categories, but not deleted.
Lastly, all posts (expired or not) can be browsed through a traditional calendar-style interface.
Does such a CMS exist? Foodies everywhere will thank you.
That doesn't sound all that difficult to implement actually. You'd just need to set up some sort of scheduled task or cron job to change the categories of posts given their expiry date. You could probably get someone to do the custom coding for that part. The rest of your requirements sound like they could be handled by just about any blog package.
Maybe you should decide on the CMS you like and work that way.