Synonyms for the term "perpetual screw" can vary depending on the context. One possible synonym may be "constant predicament". This emphasizes the idea of being continuously caught in a problematic situation, where finding a resolution seems impossible. Another synonym could be "never-ending dilemma", emphasizing the notion of an ongoing problem that lacks a definite solution. Additionally, the term "eternal bind" could be used to convey the idea of being perpetually trapped or stuck in a difficult position. Overall, these synonyms highlight the notion of a persistent and inescapable predicament, capturing the essence of the concept behind the term "perpetual screw."