I cannot top Daniel Drezner's survey of Brink Lindsay's argument, for background read that first. My thoughts run as follows...
First perhaps libertarians are not very numerous and thus they are playing against immovable opponents in the relevant political game. That is, they won’t get anything back from Democrats. That also suggests their support is worth nothing, and the decision can be viewed in that framework. I suspect this is the relevant case.
Alternatively, perhaps libertarians are numerous enough to get some concessions from Democrats. They would be playing a "threat-bluff-bargain" game with the two major parties. Isn’t a mixed strategy usually best in these settings? It becomes a question of "how much" to lean toward a party rather than "whether." Libertarians would not want Republicans to feel they were abandoned altogether. In any case the key is to act strong, offer more than you really have, and be prepared to bolt.
Keep also in mind there is a nested game within the so-called "libertarian movement." Strategies which make sense in a coordinated fashion often fail when there is discord from within. If libertarians think that the Republicans need to worry about the libertarians bolting, well, I suspect the libertarians have more than a few potential bolters of their own.
My personal inclination is not to worry too much about such matters. None of the obvious arguments, even if they appear strong, get us very far toward an answer.