Isaiah 40:29 is addressed specifically to the depleted: "He giveth power to the faint; and to them that have no might he increaseth strength." The Hebrew koach — strength — is not increased in those who still have some. It is given to the faint, the ones who have none. The starting point God works from is the empty place. The next verse — "they shall mount up with wings as eagles" — is only reached through verse 29. The soaring described in verse 31 is the result of strength given to the depleted in verse 29.
2 Corinthians 12:9 gives the theological structure for why depletion can be the place of God's power: "my strength is made perfect in weakness." The Greek teleio — "made perfect" — means to be brought to completion, to reach its fullest expression. God's strength is not most visible in the person who still has reserves. It reaches its fullest expression in the person who has run out.
Commentary is from a charismatic Protestant perspective, drawing on KJV text and public-domain sources including Spurgeon, Andrew Murray, and Matthew Henry.