Non-voting is abstinence from participation in elections. Libertarian frustration with the electoral process is understandable, given that it is mostly rigged through gerrymandering, ballot access restrictions, single member district plurality voting, the perverse incentives of rational ignorance and rent seeking, etc. The play to gradually build up the libertarian vote proportion from 1% to 2% to 4% to 8%, etc. and eventually get a majority has not worked well over the past 30 years. The level of support, at least as expressed in votes, seems to approximate something closer to a y=1% function than a y=2x, or even a y=x2 or y=x function. The question still arises, if libertarians are not going to change the system by voting, then what are they going to do? What is the alternative plan of activism that will produce liberty without the need to vote in elections any time soon?
The answer to that question is known to most libertarians, but is generally not talked about, perhaps because many are uncomfortable discussing topics such as civil disobedience and armed revolution. It is tacitly agreed that the libertarian community presently lacks the resolve, the popular support, or the resources that would be needed to do what is necessary to abolish statism and establish sufficient means to prevent a new tyrannical government from forming and instituting oppressively onerous taxes and regulations. Perhaps if those who currently favor libertarianism were willing to make greater sacrifices for the sake of their objectives, greater strides toward liberty could be made sooner; but given the current state of affairs, most activists have resigned themselves to a a long journey of gradual progress.
Experience suggests that at times, all that it will be possible for libertarians to accomplish is a slight hampering of the retrogression of society to a state of less freedom and prosperity. In light of these disheartening facts, some libertarians vote mostly as a way of satisfying themselves that they have met the demand's of Kant's Categorical Imperative. They patiently wait for social evolution, while taking advantage of some relatively easy opportunities to advance that agenda.
If the short-term decision is to either vote or not vote, it is difficult to see the superiority of abstaining from voting over voting libertarian, aside from time savings. If one votes libertarian, it sends an unmistakable message that one dissents from the two major parties in a particular way. If one does not vote, then one's nonparticipation could plausibly be construed as an indication that one simply did not care about the outcome — unless, of course, one went out of one's way to announce to the world why one was not voting. And if one is going to invest the time in doing that, then the time savings of not voting is lessened.
One way of thinking about voting is that, at this point in time, for a libertarian, it is not so much a means of controlling as a means of political speech. True, voting for a Libertarian Party candidate will not elect that candidate. But it is a protest vote. It is similar to standing outside a government building with a protest sign. Holding the sign does not change government policy directly, but it expresses an idea, registers an opinion, and helps influence others. Public opinion is shaped by that sort of action as well as many other actions.