No, it isn't a breach of contract case unless some party actually breaches the contract.
Like for example the Robertsons quitting. That hasn't happened and ain't about to.
You whole point was that Phil Robertson may have breached a morality clause that may or may not have been in the contract as you stated the morality clause to be so that A&E had a right to suspend him. That's arguable.
I don't know what the contract says. If there is a clause in the contract that has the Robertsons under contract as a group rather than as individuals, suspending one is suspending all. We don't know what the contract or contracts actually say. What we do know is that the Robertsons and in fact, everyone connected with the on-screen part of the show has indicated that if Phil Robertson is suspended they will not continue.
However, all that aside, the lawyers for A&E are spending this Christmas trying to wiggle the company out of the mess they got into because A&E has no case and no cause to suspend Phil Robertson at all.
An essential element to any claim is damages. Without provable damages there is simply no case. A&E has no damages other than what they bring on themselves. Hence, they have no case. Any action they bring is subject to a summary judgment and dismissal. Unless the Robertsons want to cross complain saying they are the ones who have been damaged. They have the better case.
Here's the way it works. If you think that the Robertsons threatened a breach by not appearing, the first thing A&E has to do is ask for assurances in writing. Assurances that the family intends to continue. If those assurances are not forthcoming, the right to sue for a breach becomes immediate. In this particular case, the right might become an obligation rather than milking the series for all they can first. Why? Because once the lawsuit is filed, the Robertsons can ask for an injunction to prevent further showing until the issues are resolved and the various rights and obligations are judicially determined.
Right now A&E's lawyers are scrambling about trying to find a graceful exit.