Strategies for tracking a disappearing ancestor

We all have one or more disappearing ancestors who "are there one census and, like magic, have disappeared the next." My second-great-grandfather is one such ancestor. For forty years we can track him with surety; then, after 1860 he drops from the record entirely. And while we can track the migration of his children from East Tennessee to Texas, we find no record of him. It is reasonable to assume he died between 1860 and 1870, except no record can be found. Also, because he remarried after his first wife's death, and at last record we find him living in Virginia with his second wife, in close proximity to some of her children, it's a distinct possibility that if he did migrate, it was with her family. So the next step is tracking totally unrelated family members in order to find any clue to this elusive ancestor; and this we have been attempting to do, but with no success thus far, given the common names of family members. But the search continues. In her article "Where Did They Go," Melissa Slate outlines the problem of disappearing ancestors and offers good advice on understanding possible reasons for their disappearance and key strategies for tracking them.