Kakashi had a Susanoo during his portion of the battle against Kaguya. And while it would seem to make sense why he wouldn't have it anymore is due to how it never really was his. It was Obito's Susanoo because those were Obito's eyes. Except that's wrong. It wasn't Obito's Susanoo, it was Kakashi's. If you look, the Susanoo has a scar over the left side of its face where Kakashi's scar is. If it were Obito's and were to include a scar, it would be on the right side of the Susanoo's face, since that's where Obito's scars were. So the inference here is that this Susanoo is Kakashi's, not Obito's. So why does he not have it anymore? Well, a common explanation would be because he no longer has the Mangekyo Sharingan. But the issue with that is that this ALSO is wrong.
Forget no longer possessing Mangekyo Sharingan, Madara no longer possessed eyes PERIOD and STILL could use his Susanoo. So this begs the question, why can't Kakashi anymore? If the Mangekyo Sharingan simply AWAKENS the Susanoo in you and doesn't actually contain it, then how come Kakashi, with his Susanoo awakened, still can't access it anymore despite no longer having Sharingan as Madara once did?