This paper by Mohammed Ansari and Lee Smolin, http://arxiv.org/abs/hep-th/0412307, seems to have been overlooked here. The authors argue that for any quantum theory of gravity (they mention LQG and causal triangulations) to produce macroscopic physics - which would be necessary for it to have GR as a limit - it has to obey a certain criterion on its renormalization group flow that is of measure zero in that configuration space. That is, the odds against this criterion being met randomly are infinity to 1. Then Ansari and Smolin try to set up an evolutionary path within complex systems theory to bring the constraint about naturally. They aren't able to prove it happens, but they show a happy outcome in a very simple example.