Hypothesis: paradoxes of time travel are possible, but (in my humble opinion) they will exhaust themselves by some smoothing into a new reality, which, in turn, will go linearly in time. In other words, the self-sustaining forever paradox of time travel is impossible.
The very description of the paradox (taken from Wikipedia)
Let us assume that such a paradox is a semblance of a self-sustained system, when an object from state A goes back in time, giving rise to state B, which makes it impossible for an object to go back in time.
This paradox may seem eternal, but in fact, objects and realities are subject to many processes that slowly dissipate their energy. For example, the resistance of the medium, gravitational radiation and even the transition in time itself. In addition, the object, having passed in time, will generate a new reality, which will cause the next reality to be generated from itself, and will not return it to its original state. Therefore, the paradox cannot sustain itself forever.