It only got stronger once, between his 2nd loss in this arc and after he was rescued from the sea. Like you explained because before he couldnt split the sky and after that he could. And it might be because he was new with it, or simply because author wanted and ignored logic. Because he was neither faster, or stronger physically, or more durable, or have some new insight about FS, or CoA. His AdCoC got stronger for no reasons. Nothing explained.
And yes, between each arc the main cast get stronger, like during all the manga. So yes, he improved his Base, his foundation, therefore his Conqueror's Haki (him doing it uncounsciously doesnt necessarily mean he improved his lvl, he only got a new way of use it).
But here we are talking if he improved his Conqueror Haki between chapter 1042 and chapter 1044 and there's no proof of that. A new form is not, not for now for the reasons I explained.