A special case: [Dynnikov and Veselov][1] found perfect Morse functions on $G=O(n), U(n), Sp(n)$. Since $Sp(n)$ is simply-connected, their theorem answers your question in this case. See Theorem 1.1 3) of their paper to see that all critical points of the Morse function on $Sp(n)$ have index $0$ or $>2$. 

One could try to modify their technique to find perfect Morse functions on $Spin(n)$ or $SU(n)$, and thus answer your question in these cases.  


  [1]: http://arxiv.org/abs/dg-ga/9506004