I'm not an attorney and you may need to consult one - however contracts usually go like this.
If its written in the contract, then you'll have to pay it. If its not written in the contract that you either agreed to pay it, or if it was written you would and the agent waived it, then you won't.
However, if nothing is written about the Buyer's agent fee anywhere, no Buyer's Agency Agreement, not in the sales contract, etc., then the agent is going to have a hard time getting you to pay it. Also, the buyer's agent usually doesn't have the power to prevent the closing, certainly not over a fee. The agent's recourse would usually be to sue you. You may want to call their broker.
You didn't say why the closing date had come and gone. Are you still in escrow? What else is holding up the closing? The only things that normally hold up closing are funding on the buyer's side, title issues on the seller's side, on a short sale the seller's lender having final review of the HUD1, etc.
Anyway, check everything you signed to see if its written down and addressed, one way or the other. And if its not, start with the agent's broker then proceed to a real estate attorney.