if I remember correctly, it's in TGS that Moridin says that there is a right time for Rand to die. That being said, we know there is a connection between Rand and Moridin so that could be a reason he doesn't want him dead but at that time in the book, Moridin doesn't seem aware that they are connected so that shouldn't matter. What's the reasoning for keeping him alive? Is it to try and drive Rand into deeper madness for the DO to take control or something else?

He is aware. Moridin says (in the SAME chapter) "I'm so tired. Is that because of me, or because of you?"

so do you think he's aware of the eventual merging?

I'm not sure he's aware of that. But Rand isn't either.