Finding the right synonyms for the phrase "ongoing conundrum" can be tricky as it is a complex term. Some possible alternatives to this phrase include "never-ending puzzle," "perennial mystery," "continual enigma," "persistent dilemma," or "unceasing paradox." All of these synonyms convey a sense of something that is ongoing, unresolved, and difficult to solve. Whether you are writing about a political situation, a scientific problem, or a personal challenge, these synonyms will help you to express the complexity and persistence of the issue at hand. So, next time you're stuck in an ongoing conundrum, remember that there are always alternative ways to express your frustrations and uncertainties.