This is not necessarily a problem - in a quantum mechanical formulation, it's simple enough to resolve (for instance) a grandfather paradox by looking at quantum interference around causal loops (almost 100% analogous to the way interference on a violin string will restrict stable modes to certain frequencies, interference around a causal loop will only allow stable self-sustaining situations to survive, so any grandfather paradox would self-interfere and not be allowed). The main difference is that with closed timelike curves the quantum effects can get a lot stronger than without them, even affecting very large objects.
