This post is a bit late. Mohamed Anber and I have written a paper that provides counter-examples to the idea that there is a running gravitational coupling. Here is the link. We feel that this is a crucial rebuttal to the idea of a running gravitational coupling in the perturbative region. If this problem extends past the Planck scale, then it would seem that there would be problems for the idea of Asymptotic Safety.
18 02 2012