LOL... Kswild, maybe I'm interpreting it wrong, but was under the impression that he couldn't shoot because the deer were running, not the hunter.

Excellent advise Flags... Often deer will run because another deer got alarmed, without knowing why the initial deer became alarmed. Sit tight and see if any of them circle back. Also as Flags pointed out, there is a reason those deer were there, other deer may come there for the same reason.