Though it might not be explicitly stated in the paper, EPaxos has the same liveness guarantee as all other consensus protocols: commands will eventually commit if a long enough period of synchrony occurs. As the author of this post notes, this is a fundamental limitation of the specification of the consensus problem - no protocol can get around the limitation while solving consensus by definition.
This is unclear to me. Egalitarian Paxos guarantees progress under a full asynchronous model and doesn't have the dueling leaders problem. So this looks like a weakness of standard Paxos itself, not a fundamental problem.