I have background in this pretty extensively (at least compared to my background anywhere else) and can't resist adding a few thoughts.
1. Many of the existing denominations that still meaningfully hold to a Reformed confession arose from an act of ecclesiastical separation. The OPC, the PCA, and the URC, for instance, all divided from a connection in which they used to exist. The Reformation involved a lot of separating from existing connections.
2. Ecclesiastical separation is witnessed to in various parts of the New Testament. E.g., Romans 16:17, Titus 3:10, 2 John 10 are all relevant.
3. Ecclesiastical separation is simply church discipline for the ecclesiastically disenfranchised. In other words, if false teachers can't be put out of the church because they've taken control, what recourse remains to those who would be faithful? The move of disfellowship looks different when it's a faithful minority, but the principle is the same.
Denying those facts doesn't help answer what might be called divisive or pugnacious or fundamentalistic separatists. Of course separation can be practiced in imbalanced, sinful, fleshly ways. In my own opinion, there has been a lot of very fleshly pride in being perceived as godly in some of the separatist movements in the US, and that desire for reputation has both enabled and concealed many appalling abuses. But the separatist also has a conscience that has been partially informed by the word of God, and in calling them to a better way, there should be no attempt to make them give up what they have attained or the proper rule they have received. They may need to learn in addition about the sinfulness of schism, about the difficult labor of reformation, about not confusing personal impatience with God's judgment, but that doesn't mean they have to become spineless ecumenists who associate in ecclesiastical fellowship with heresy, and so forth.
Many people within the movements known for an emphasis on Biblical separation have come to see that there was sometimes an inappropriate unity within their ranks. As long as someone had a "separated" ministry (separated from the WCC, the NAE, the BGEA, and a number of other organizations depending on who had come on their radar) doctrinal weakness and personal bombast didn't matter. It is a danger with any dearly-held distinctive, that we'll embrace others who agree with us on that, even if we're worlds apart on other points. But that's an argument for maintaining the whole circle of what we know and not improperly privileging one doctrine or distinctive to the detriment of others, not for giving up on that particular point.
The idea of 'secondary separation' has been held up for a lot of ridicule. But once you grant the premises, you can see how the logic of their position suggests something like it. So, first, Biblical separation requires us to dissociate ourselves from those who are persistently and impenitently unfaithful. Second, ongoing failure to practice Biblical separation is an instance of persistent and impenitent unfaithfulness. Third, then, Biblical separation requires us to dissociate ourselves from those who fail to practice Biblical separation, Q.E.D. Now that is rather two dimensional, and tends to think far too much in terms of isolated congregations and individuals; but it's hardly incomprehensible how people could follow that line of reasoning and feel constrained to disfellowship from more and more and more.