Maximal non-reducible vertex cover of a graph
What you call a non-reducible vertex cover is commonly known as a minimal vertex cover. So, what you are looking for is a minimal vertex cover of maximum cardinality, i.e a maximum minimal vertex cover.

I'm not aware of any literature on this problem per se, however the equivalent Independent Dominating Set problem is quite well studied. An independent dominating set in a graph $G$ is an independent set $I$ such that every vertex not in $I$ has a neighbor in $I$. In the Independent Dominating Set problem input is a graph $G$ and the task is to find a smallest possible independent dominating set. This problem is known to be NP-complete. 

The two problems are equivalent because a set $S$ is a minimal vertex cover if and only if $V(G) \setminus S$ is an independent dominating set.