There are too many factors to consider to answer this thoroughly. That said, there is at least one consideration.
Google does not cap sending users to any site.
That said, if a new post is discovered by Google, Google will "taste" the post by defaulting some of the pages metrics high enough that it will appear relatively high in the SERPs. The reason for this is simple. If tasting is not done, no one would ever see the new pages and Google would never be able to test the pages performance in the SERPs.
Google does want diversity in its SERPs and will limit how many SERP links it provides to a site on a single SERP page or search query. This means that if a new post competes with other existing posts, then the new page will push at least one post out of the SERPs temporarily while the new page is tasted.
As new posts are "tasted", the metrics of the page will change according to metrics such as CTR (click through rate), bounce backs, performance of surrounding SERP links, on site signals such as how far from the home page the new post is (clicks it takes to get to the page), etc. As the new posts settles into a position where it should perform based upon the metrics, your older pages should return to normal performance.
Again, there are many factors that effect older posts when a new post appears such as cannibalization and distance from the home page. Many blogs will post newer posts on the home page while older posts drop from the home page changing the importance of each page.
There is a lot to consider, but do know this. Any post, especially on smaller sites, will represent a disruption, however, this disruption is temporary as Google adjusts the metrics of each page. This could take a while, however, any older post should return to where it should be placed based upon metrics within the SERPs.
