Jim Henley suggests individual trade-offs here, of the form "If [loyalist progressive] wants [disgruntled anti-militarist] to vote for the Democrats, then [loyalist progressive] should trade that person something they want, like a letter to a politician." The basic problem with that is that signatures on petitions, letters to politicians, and so on are valueless. We've already determined that -- that's a major reason why movements like Occupy spring up. Petitions, letters, one-day protests and so on don't cause anyone to do anything. So trading a valueless political action for a valueless vote is like some kids pretending to play poker but they can't really keep track of whether one red chip is worth 5 black or vice versa.
Let's consider the disgruntled anti-militarists as a bloc, at least in potential. They're not negotiating with individual Democrats. They're negotiating with the Democratic Party. The Democratic Party has the power to give them at least some of what they want, in the form of actual changed policies. And the anti-militarists, at least in potential, would have the power to give the Democratic Party what it wants, in the form of won elections.
In fact, the disgruntled anti-militarists are not a bloc, and do not have the power to make a difference in elections, mostly because most people in America like war, assassination, and torture, or at least don't see why anyone but a nut would object very strongly. So we have a trading situation going through supposed middlemen (i.e. the individual voters or letter-writers) in which none of the middlemen have the power to carry out the deal. I don't think you need to have a libertarian background to see why this may not be a good idea. "Here, kid, I'll give you 5 black chips for your red one. Aren't you happy now?" You might equally well object that the red chip is valueless too, so if there is condescension or futility it's going both ways. But.
But the important part of not voting is to say that you're not playing the game. People want the reassurance of knowing that settled, middle-class people with young children, like me, are still dutifully going through the motions, and are not seriously saying that maybe it's time that we just stopped supporting the whole American political system. That's what you lose if you trade the red chips for the black chips. And that's why I don't expect there to be a lot of people taking this deal.