The eternal worshipper theory is pretty entertaining though; it seems like something clever Athena, who is touted for her intellect, set up to perpetuate their existence. Plus, are we sure that direct acts of worship is what keeps them alive or gives them power? For all we know, it might just be faith, belief and other directed feelings/thoughts (admiration, awe, fear, respect) instead, which Asterion is not lacking in any regard. Maybe eternal believer would be more fitting?
Also, I think I can counter one of your points of thinking that Asterion would forego the gods-- both collectively and individually. They've sentenced and deemed Asterion to be meek and timid-- submissive to the wills of the gods and higher powers. Perhaps Athena thought that this mentality is eternally cemented in Asterion's character. In fact, this proves true; Asterion found himself genuinely deserving of his sentence all this time. A perfect personality to serve as an eternal worshipper, no? Asterion knew that the torturous labyrinth is the collective efforts of the gods (Athena included). What could the prisoner do but continue believing in the power, existence and dominance of its creators as the reality of his experience in the labyrinth is continually proven to him everyday all these years? If the gods are indeed fed by this kind of belief, then the labyrinth is an ingenious self-sustaining system. Just to add, I don't remember Asterion harboring contempt on any of the gods. He's placed them on such a high pedestal that he probably can't even start to think of forsaking them-- he'd probably supplicate himself to them more. I swear, this may be an intentional big brain move on Athena's part-- taking advantage of his personality and all.