According to our current understanding of physics, many models that allow for closed timelike curves (CTCs) are indeed considered unstable against perturbations. A closed timelike curve is a theoretical construct that would enable time travel by allowing an object to return to its own past.
One of the most well-known models that permits CTCs is the Gödel metric, which is a solution to Einstein's field equations in general relativity. In this model, spacetime possesses a certain type of rotation that creates closed timelike curves. However, it has been shown that the presence of CTCs in the Gödel metric leads to various instabilities and causality violations.
Furthermore, the famous "chronology protection conjecture" proposed by physicist Stephen Hawking suggests that the laws of physics themselves prevent the formation of CTCs. This conjecture is based on the idea that the occurrence of CTCs would create inconsistencies and paradoxes, violating causality and leading to logical contradictions.
While there are some speculative ideas and theories that explore the possibility of stable CTCs, such as through the concept of "self-consistency," these remain highly theoretical and are subject to ongoing debate and investigation. At present, there is no consensus among physicists regarding stable CTCs or practical methods for achieving time travel.