I have a big strange problem with a site with k2 2.7.1 and Joomla 3.6.5 (now but problem persists since 1st version of 3.6.x).
Server have PHP 5.3.29, MySQL 5.5.52-cll

The problem is that on only 1 category new items refuse to show on Front End. I deleted the category, recreated, made clean install of Joomla files and K2, checked DB, done everything. Checked if new items have language selected to ALL (even site is mono-language).

That items (articles) in that particular category refuse to display on front-end....

Any help please ..

Double the check the category's (and the menu item's) settings to see if you have any errors, e.g. show only featured items.

I have checked many times, I even made new items featured yet they still refuse to show-up.

Done all you could imagine. Just a side note: I am making sites with Joomla since was Mambo, I even was part of VirtueMart years ago.

I have checked for Java Scripting problems, etc.

So everything is working properly apart from one category.
This is really weird.
Have you enabled browser caching?
Any weird htaccess rules?