Isaiah 40:29 — "He giveth power to the faint; and to them that have no might he increaseth strength" — comes before the famous "wings as eagles" verse. The starting point God works from is not the soaring person but the faint one, the one who has no might left. The Hebrew koach — strength — is restored to the ones who have exhausted theirs, not to the ones who still have reserves. Foster care burnout is precisely this exhaustion, and it is precisely the condition this promise addresses.
Matthew 25:40 records Jesus' identification with children who are vulnerable: "Inasmuch as ye have done it unto one of the least of these my brethren, ye have done it unto me." The children in your care are specifically the ones Jesus named when he said "the least of these." The work of foster parenting is not service rendered to a category — it is service rendered to Jesus, and he keeps account of every meal, every night, every goodbye.
Commentary is from a charismatic Protestant perspective, drawing on KJV text and public-domain sources including Spurgeon, Andrew Murray, and Matthew Henry.