I would contact the person to whom I sent a counter and asked them to let me know as soon as possible if I received another offer and told them the time frame I needed a response or I would move on. To me that would be the honorable thing to do.Then as a seller, you must put the other offer on hold, and give him time to rethink and withdraw his offer, and then the guy you countered says no within the "time frame." Now as the seller, your item is still "for sale."
Your scenario would probably work among friends, but not on an open market. Suppose you make an offer on a used car, then the owner counters, but you leave to think about it, and when you return, the car has been sold. As Pbnaudio said, "You snooze you loose."
IMHO, if I gave someone a counter offer, and did not hear from them for half a day, I would assume the answer was no, regardless of Audiogon's time frame.