So, I discussed this with my French girlfriend.

“Still” would be translated as “toujours” in this case – the implication is that it’s been happening continuously. “Encore” is sort of like “again” – it would signify that the person stopped sleeping, woke up, then went back to sleep. So:

Est-ce que tu dors TOUJOURS ?

If this were said out loud (like an angry parent talking to their teenager), they would probably just say “tu dors TOUJOURS !?” or “tu es TOUJOURS endormi !?” (“you’re STILL asleep!?”), using tone of voice to signify the question.

It’s not necessary to be precise about the “am sleeping” part by using “…en train de…”, unless you really want to stress the continuity of the action. But the difference here would be even more subtle than the toujours/encore difference.

« Dors-tu encore ? » or you could say too « Es-tu toujours endormi ? »
Encore and toujours meaning still.

Hmmmm… “Es-tu toujours endormi?” might be seen also as deprecatory. Meaning: “Are you always so asleep as not seeing anything?!?!? (or whatever was expected)?” In fact, in that case “Dors-tu encore?” is a more accurately translated by: Are you still asleep?

Out of any context, a plain “est-ce que tu dors encore?” comes to mind.