Which binary search trees have constant time rebalancing time at min/max?
Consider a constant set of $k$ insertions done directly at the max node, and the left and right sub-trees of the root node ($L$, $R$). If each rebalancing operation required only constant time, then only $O(\frac{log(n)}{k})$ of the inserted elements could be in $L$, since the maximal element is a leaf and the tree is balanced. 

While this simple analysis is incorrect for non-constant $k$, the intuition still holds - if rebalancing after max (/min) insertion was always constant, repeated max (/min) insertions would cause $R$ (/$L$) to grow larger, and the tree could not be balanced.