Where an offer is governed by an option contract, the offeror cannot terminate the offeree's ability to accept the offer by revoking the offer.
Consider this variant of the Rex/Regina example: Rex offers to sell his car to Regina, and she says she would like to have some time to think about it. Rex responds by making a legally enforceable promise to hold he will keep the offer open for six days. Three days later, Rex gets an offer from Jones to buy the car for double the price in Rex's offer to Regina.
The day he gets Jones's offer, Rex hand-delivers a letter to Regina in which he asserts that he is revoking his offer to sell her his car.