Ron W.: good question--nice thread!
Diongsis: thanks for the ref. to the '59 booklet. I wonder how much or how frequently it occurred in the WTS pubs before the NWT appeared. Apparently in 1953 Fred Franz repeated the old KJV rendering at Gen 49:18 where the speaker Jacob uses the phrase when blessing Dan. But it is biggest in the Psalms (for example, 42:5, 11; 43:5; 62:5, etc.). It also appears at 2 Kings 6:33 in a bad way. Perhaps it was some common idiom in Israelite/Jewish society even without God being involved (Job 14:14)? It looks like it was a regular way Jews viewed their God: hang in there, even for a long time, until God intervenes. The concept seems to lie behind the people's expression, "God has turned his attention to his people," after Jesus resurrects the son of the widow of Nain (Luke 7:16).
In the modern Witness world it's not the sort of expression that is taught to newbies, but it's one of those many concepts that one is supposed to learn as one "matures" in the org. There are so many of those!
SBF: the ref. to the exact song and which songbook might be helpful in dating the expression, esp. if it's a song that was carried over from an earlier songbook.