Well, you have to figure that the entire nerve can't be completely dead (I'm not experienced in this, but I gather there has to be a point somewhere where the nerve picks back up and is living, again, as it gets back to the central nerves).
Is there a possibility the pain could be coming from the gum area beneath or around the crown and it's just indistinguishable from tooth pain because of the location? Have you seen your dentist again since the crown fitting?
If your next cleaning is less than a month away, you may just want to hold out, see if it gets better and mention it on cleaning day if it doesn't. If it isn't, you may just want to ring them up and mention that you're still having some sensitivity when you tap the crown; they may be able to suggest something or they may want to see you to make sure everything's alright.