(a) That's right. If there is an anticipatory breach of an entire contract, or of a condition in a contract, or a repudiation of an innominate term which would amount to a serious breach, the non-defaulting party has the right to terminate performance immediately, even before performance is actually due.
However, the non-defaulting party may elect to continue with the contract despite a serious anticipatory breach, hoping that performance will be made when it becomes due.
A party who wishes to terminate performance on grounds of anticipatory breach must decide to do so within a reasonable period of time. A decision to terminate must be communicated clearly to the other party by words or conduct. If a party attempts to terminate performance of a contract on grounds of anticipatory breach, but they are unable to prove a sufficiently serious breach, their action of terminating performance will itself amount to an act of repudiation, leaving them open to an action for breach of the contract.
In the example, B clearly repudiated the contract, but A did not accept the repudiation. He clearly stated that he intended to hold B to the contract. This decision left it open to B to change his mind and perform the contract. Having made the decision not to terminate performance on grounds of B's anticipatory breach, it is too late for A to reverse that decision.