Please ignore all other blocks and just select the Horse Racing category. In the showcase module linked above you will see there is only one item registering in this category titled Saturday 2 March. However, if you go to the page where this category is displayed as a default category blog layout (
) you can see that there has been a new item added to that category which doesn't show up in Digi Showcase.
I can't find any tools that would govern this behaviour in the module settings, and I have cleared cache and checked with other browsers from different IPs and it still isn't there.
If Joomla has no cache, as well as the web server has no cache for generated pages, the module should show new articles immediately after you have created and published them. You don't have to wait even a minute.
So if your articles are not displayed immediately, it's mean that, somewhere, there is a cache which doesn't allow to the module to parse new articles from the database on every page refresh. You must find that option and disable it.
Anyway, ensure that the module has enough articles displayed to match your needs.