Denial-of-Service (DoS) threats pose a major challenge to the idea of physical-layer key generation as the underlying wireless channels for key extraction are usually public. Identifying this vulnerability, we study the effect of DoS threats on relay-assisted key generation, and show that a reactive jamming attack on the distribution phase of relay-assisted key generation can forbid the nodes from extracting secret keys. To circumvent this problem, we propose a self-sustainable key generation model, wherein a frequency-hopping based distribution phase is employed to evade the jamming attack even though the participating nodes do not share prior credentials. A salient feature of the idea is to carve out a few bits from the key generation phase and subsequently use them to pick a frequency band at random for the broadcast phase. Interesting resource-allocation problems are formulated on how to extract maximum number of secret bits while also being able to evade the jamming attack with high probability. Tractable low-complexity solutions are also provided to the resource-allocation problems, along with insights on the feasibility of their implementation in practice.