Isaiah 40:31 is often quoted as a general encouragement, but its context is specific: it follows a diagnosis of Israel's condition — "The LORD... is not weary" (v.28), followed by the observation that "the youths shall faint and be weary, and the young men shall utterly fall" (v.30). Even the young and strong will collapse. The promise of renewed strength is explicitly addressed to that reality — not to those who have managed their energy well, but to those who have genuinely run out. "They that wait upon the LORD shall renew their strength" — wait, not perform.
Galatians 6:9 contains both a warning and a promise: "And let us not be weary in well doing: for in due season we shall reap, if we faint not." The Greek egkakomein — "be weary" — means to lose heart, to give up from exhaustion. Paul is writing to people who are already weary. The promise of a harvest in due season is specifically attached to not fainting — which implies the temptation to faint is real and pressing.
Commentary is from a charismatic Protestant perspective, drawing on KJV text and public-domain sources including Spurgeon, Andrew Murray, and Matthew Henry.