General relativity does not seem to prohibit time-loops (called closed timelike curves by physicists), but quantum theory might prohibit these, This is what Stephen Hawking thought.
Stephen Hawking: "It seems that there is a Chronology Protection Agency which prevents the appearance of closed timelike curves and so makes the universe safe for historians."
This roughly states that near the boundary in spacetime where time-loops form, the energy for quantum fields blow up (e.g., infinite blueshift), thus preventing (by wall-of-fire barriers) physical objects from crossing into the region where there are time-loops. There seems to be some semi-classical (part classical, part quantum) evidence for this conjecture, but a more refined analysis by Kay, Radzikowski, and Wald muddies the picture a bit. Their analysis shows that the energy is ill-defined, but not necessarily infinite, at such a boundary.
This may be just an indication that the semi-classical theory breaks down at chronology horizons, and that full quantum gravity is needed for definitive predictions.