The half-lives of both zero-order and second-order reactions depend on both initial concentrations and rate constants. Why does the half-life for second order decrease with increasing initial concentration

This is because the half life of second order reactions is inversely proportional to the initial concentration of the reactant.

Explanation:

The equation to half life in the second order reactions is given by:

t1/2=1/[A]initial

From the equation, you can see that as the initial concentration of A increases the denominator also increases ,thus overall value (t1/2) decreases.

Hope this helps:)