We have put products into our store.

We set the start dates and end dates on both products some with variants and some without.  It seems like the products should unpublish when the end date passes. But this does not happen.  It does remove it from the front end product list, but in the admin they are still flagged as published. and if you type in the physical URL into the browser the product is still published.  

I am having to go in manually go to the admin panel and unpublish products so that search engines and other users will not see them if they just happen to come across them.  

So which date field is controlling the publish and unpublish. And if we have variants that all end on the same date, do the variants control the product publish flag or does something else.  

We are confused on what exactly controls the product to become unpublished, beside just manually going into the admin and flipping the flag ourselves.