If one were to extrude the space-time continuum along a fifth dimension, and define existence as the limit at infinity along this dimension, then any time travel would be unstable and would never persist until infinity. Whatever effect a future event had on the past would alter time to prevent the future even from ever taking place (this is along the extruded dimension so that is “possible” to alter time). As you proceed along the extruded dimension till infinity, circumstantial changes accumulate until at some point the effect of those changes changes future circumstances enough that the time travel doesn’t occur. At that point the discontinuity in space-time collapses.
This thought experiment demonstrates how there could be instabilities in existence. Even if you discount the fifth dimension, the fact remains that the time travel would have to have exactly the effect on the past that produces the circumstances that led to the time travel taking place. If even a small circumstance differs from that that time travel cannot exist.