Smart Search creates a "snapshot" of published K2 items in its index. Until it refreshes its index, if you change the published state of some K2 item, it will not reflect immediately.

If, as you say, this occurs in standard Joomla search (the com_search component), then this could relate to aggressive server-side caching, because upon showing the results, Joomla does a "GET" request, which can easily be cached by software like Varnish or Nginx (if it's setup in your server of course).