So as I expected, there is some sort of rationale that the Society gives for the rendering. I do however doubt its applicability. First of all, there is a mismatch in the lexical semantics of the stative verbs chyh "live" and chzq "(be) strong" in the purported parallel of Exodus 1:17 and 4:21. Both are fundamentally stative verbs that secondarily express changes of state (i.e. "become alive, enliven" in the case of chyh and "become strong, strengthen" in the case of chzq). In Exodus 4:21, the piel imperfect clearly expresses a change of state as the NWT itself indicates ("I shall let his heart become obstinate"). But in Exodus 1:17, there is no real change of state in the case of keeping someone alive or preserving them, so the factitive force may be weak as it is in this passage (see especially 1:22, where the female children are singled out from extermination; cf. also Genesis 12:12, Numbers 31:18, 2 Samuel 8:2, Jeremiah 49:11, etc.) or strong as it is in Genesis 6:19 (where Noah acts to preserve the seed of the animals), Genesis 19:32-34 (where the daughters of Lot act to preserve his seed), 1 Kings 18:5 (where Ahab and Obadiah act to keep their horses and mules alive by finding grass for them), etc. It is rather a matter of maintaining the state in the face of possible change. The nuance that the Society mentions thus pertains to the stative sense of the verb; one does not necessarily have to act to keep the state going but only permit the state to continue on its own.
But the same verb could also express a deliberate change in state, cf. the piel imperfect in Deuteronomy 32:39 where God acts to make one alive (just as he kills, wounds, and heals, all similar changes of state), the piel imperfect in Nehemiah 4:2 which has the Jews reviving the walls out of the ruins, the piel imperfect in Isaiah 7:21 which has a man nourishing a young cow, etc. It is this pattern that nicely fits the usage in Exodus 4:21, which has a piel imperfect verb that expresses a change in state. So it is a little odd that the parallel is sought with a use of the verb that has mainly stative force. Indeed there is a good parallel between God acting to make firm Pharaoh's heart and God acting to revive (i.e. the change-of-state usage of chyh) the heart of contrite persons in Isaiah 57:15:
Exodus 4:21: "But I will strengthen his heart ('ny 'chzq 't-lbw) so that he will not let the people go".
Isaiah 57:15: "I live in a high and holy place, but also with him who is contrite and lowly in spirit, to revive the spirit of the lowly and to revive the heart of the contrite (l-hchywt lb ndk'ym)".
While this is more causative than factitive (i.e. hifil instead of piel), it shares with Exodus 4:21 a verb that implies a change of state and has "God" as the actor and the "heart" as the thing that is acted upon. So going back to the verb chzq, we could compare the piel imperfect in Ezekiel 34:16: "I will search for the lost and bring back the strays. I will bind up the injured and strengthen the weak ('t-hchwlh 'chzq), but the sleek and the strong I will destroy". This does not mean that God would merely permit the weak to become strong on their own accord, without any action on God's part. The sense clearly is that God would impart strength to these people, just as he would act to destroy the strong and bind up the injured. See also Ezekiel 30:24: "I will strengthen the arms (chzqty 't-zr`wt) of the king of Babylon and put my sword in his hand, and I will break Pharaoh's arms". Here the piel has the factitive force of bringing about a new state of strength in Nebuchadnezzar's arms (reinforced by the reference to God actively putting a sword in his hand), a state that brings about the breaking of Pharaoh's arms. And while chyh allows the piel to express a state that continues through one's action or inaction, I can't find a similar usage with chzq. The passages that semantically indicate a state that actively maintained seem to usually involve the hifil (cf. the sense of holding something fast in Judges 7:8, Job 2:9, etc.), not the piel which involves a change in state, and I can't find an instance of someone allowing or permitting a state of strength/force/firmness through inaction. But I could be wrong here.
So why doesn't the NWT say "I will let the arms of the king of Babylon become strong" (as opposed to "And I will strengthen the arms of the king of Babylon", NWT), or "I shall let the weak become strong" (as opposed to, "the ailing one I shall strengthen", NWT), or any other case where the verb has factitive force? Why is Exodus 4:21 parr. a special case? Could it be that there is a theological Tendenz on the part of the translators that found the text troublesome? The passage as it stands is sometimes thought to present an exegetical problem when it comes to the issue of free will. As it reads, it could suggest that God may interfere with a person's free will (tho this is not a necessary interpretation, as there is no similar issue when it comes to God enlivening the hearts of the downtrodden in Isaiah 57:15). It is thus possible that the NWT translators and Rotherham appealed in this case to special pleading to make the apparent problem disappear from the text.
Anyway, that's my guess based on my (incomplete) knowledge of the factitive use of the piel in Hebrew (the other uses don't seem to be relevant). Maybe Narkissos or Alleymom or mebaqqer could add to or correct what I've written.....I would be really interested to know if there has been a study of the semantics of the different stem forms of chyh (e.g. qal versus piel versus hifil in the active/stative paradigm) that comments on the usage in Genesis 12:12, Exodus 4:17-21, Numbers 31:18, 2 Samuel 8:2, etc.
