どうやって is like "by doing what" — it is an interrogative to ask about a means to accomplish something. どうやってまだ立ってるんだ would be a natural question if you think there is some kind of trick involved, such as when someone is happily standing in the air even after the ground has completely disappeared.
But if you are talking about someone who is still standing after being badly beaten in a boxing match, there is no special trick involved, so なぜまだ立っていられるんだ or どうしてまだ立っていられるんだ sounds a little more natural to me. (Potential form is not strictly necessary, so どうしてまだ立ってるんだ is fine, too.)
(Don't forget to always use an explanatory-の in a why-type question!)