The reason the south bit the bullet in 1861 was that it was the last time they could hope to pull it off before northern industrial growth went totally out of control, king cotton was deposed forever, and the generation of military geniuses produced during the Mexican-American War retired or died. If a secession crisis had occurred in, say, 1855, luck might have been more on their side. The question of "now what?" after successful secession is a different one entirely though.
I would say that, if they were too chicken in 1861 and continued to try and bide for time, barring a major industrial revolution in the south (which might have spelled the end for slavery anyway and defeated the whole purpose of secession), they would have become overwhelmed quicker with each passing year and with fewer potential allies. The last time I could see them trying in this scenario is maybe 1875, by then they're totally outmatched economically, slavery is dying, their great generals would be dying, and they would be totally isolated in the rest of the world.