When is a “covenant not to compete” not enforceable?

The answer to this question depends almost entirely on the law in the particular state law governing the agreement (and the agreement will specify which state law governs). Each state has a different approach to enforcing these agreements. Some states consider them to be almost always unenforceable as illegal restraints of trade and some states uphold them if they are reasonable in time and geographic area and are necessary to protect a legitimate business interest. It is a very complicated area of the law and in this instance, you need to consult a lawyer.