UPDATED June 16, 2014:
You can capture some of the flavor in the following discussions:
"When one introduces realistic clocks, quantum mechanics ceases to be unitary and a fundamental mechanism of decoherence of quantum states arises. We estimate the rate of universal loss of unitarity using optimal realistic clocks. In particular we observe that the rate is rapid enough to eliminate the black hole information puzzle: all information is lost through the fundamental decoherence before the black hole can evaporate."(http://arxiv.org/abs/hep-th/0406260)But, while "unitarity" has a usual meaning in quantum mechanics to the effect of, all the calculated probabilities of different possibilities add up to 100%, it isn't totally clear that this is real what the authors mean when they talk about unitarity in this context. As Physics Forum moderator Marcus explains:
"...general relativity is a generally covariant theory where one needs to describe the evolution in a relational way. One ends up describing how certain objects change when other objects, taken as clocks, change. At the quantum level this relational description will compare the outcomes of measurements of quantum objects."(http://arxiv.org/abs/gr-qc/0603090)
"...as ordinarily formulated, quantum mechanics involves an idealization. That is, the use of a perfect classical clock to measure times. Such a device clearly does not exist in nature, since all measuring devices are subject to some level of quantum fluctuations. The equations of quantum mechanics, when cast in terms of the variable that is really measured by a clock in the laboratory, differ from the traditional Schroedinger description. Although this is an idea that arises naturally in ordinary quantum mechanics, it is of paramount importance when one is discussing quantum gravity. This is due to the fact that general relativity is a generally covariant theory where one needs to describe the evolution in a relational way..."(http://arxiv.org/abs/quant-ph/0608243)
So then the question comes back: what does "unitary" mean, in this field theory context, where we no longer have a "wave function" telling simply the amplitude of a particle to be at some particular place at some moment. I think now unitary means more something like preserving information, or preserving coherence, predictability. It is not as clear what the intuitive meaning is.It is also not clear how much of the "fundamental decoherence" that arises when you try to migrate ordinary quantum mechanics from 4 dimensional Minkowski space where only special relativity holds to the space of general relativity is actually a physical effect, and how much of this is really a function of not being clever enough in how quantum mechanical equations are generalized into a general relativistic context.
Obviously, to the extent that a loss of unitarity takes its conventional meaning of the probability of all possibilities adding up to 100%, we know that in the real world, (whose "equations" are properly formulated) the probabilities of all possibilities still do add up to 100%. We don't get "blue screens of death" where the numbers simply don't add up and "nothing" happens, or more than one outcome happens simultaneously, in the same universe, in the real world.
But, it could be that the lack of the fixed time scale in general relativity and the probabilistic nature of quantum mechanics, do conspire in the real world to erase "information" that would otherwise be preserved in either of those theories acting alone, although I suspect this might an ambiguity between two or more possible sets of information, rather than infinitely many possibilities, in the real world absent highly contrived circumstances that would never actually occur.