If a counter offer is made on a contract signed by the buyer and the buyer refused to sign the counter offer, what is the status of the original offer?
If your Buyer refused your counter offer then there is no longer an offer to purchase. If you would have accepted the initial offer then the Buyer would be obligated to perform.
When you counter "back" to a Buyer, then the original terms of the Buyer's offer have changed. The Buyer then has the option to either accept your counter or decline, just as you had the opportunity to accept or decline the Buyer's original offer.
It appears that the counter offer is unacceptable to the Buyer; therefore, the only recourse you may have, if still available, is for your agent to contact the Buyer's agent and ask if they would be interested in submitting their original offer again. However, this is not a position of strength for a Seller.
It may be more beneficial for your agent to "test the waters" with the Buyer's agent and see if it could be determined why the counter offer was unacceptable. If you then feel you could accept the change the Buyer balked at accepting perhaps, with a deft touch, your agent will be able to gracefully suggest you may consider dropping that particular issue if the Buyer would like to submit without that condition.