I still think it's either about cups or about lack of any viable alternatives willing to inherit this mess mid season. But IF it's neither, then I'm inclined to think that Levy's clinging on to him as his next miracle worker a la Pochettino. It also aligns more or less perfectly with what some people here expect from Ange, so the notion of Levy thinking along similar lines isn't far fetched.
The obvious question is why. Why him, and not anybody else? Did Levy fall in love with him during that magical 10 match spell, and now refuse to let those fond memories go? That's the antithesis of how Levy usually operates. Is it Ange's captivating aura as this know-it-all ideologue who also happens to be very modest in his demands, in total contrast to Mourinho and Conte? A low maintanence manager is always welcome to any chairman, and Ange in particular certainly knows how to talk the talk, but I doubt that these would be enough to keep Levy calm after everything that has happened in the last couple of months. 1 point from 7 league matches, getting outplayed by relegation fodders in the process, dropping to relegation zone are all extremely difficult to swallow, no matter how you look at it.
Like I said, chances of him getting the boot after Liverpool or Villa are substantial. But if he somehow avoids it, and in fact starts the next season as well, what I outlined above based on Levy searching for another Pochettino might be a plausible explanation.