quantum field theory - Why is $R^2$ gravity not unitary?

I have often heard that $R^2$ gravity (as studied by Stelle) is renormalisable but not unitary. My question is: what is it that causes the theory to suffer from problems with unitarity?

My naive understanding is that if the the Hamiltonian is hermitian then the $S$-matrix $$ \langle \text{out} \mid S \mid \text{in} \rangle = \lim_{T\to\infty} \langle \text{out} \mid e^{-iH(2T)} \mid \text{in} \rangle $$ must be unitary by definition. So why is this not the case for $R^2$ gravity?

I see that Luboš Motl has a nice discussion related to such things here, but I am not sure which, if any, of the reasons he mentions relate to $R^2$ gravity.

Are there other well known theories that have similar problems?