Matthew 18:10 contains a statement from Jesus about children that is easy to read past: "Take heed that ye despise not one of these little ones; for I say unto you, That in heaven their angels do always behold the face of my Father which is in heaven." The Greek word for "always" — diapantos — means continuously, without interruption. The children have angels who are in continuous audience before the Father. The child facing illness is not outside continuous divine attention.
Psalm 91:11 says "he shall give his angels charge over thee, to keep thee in all thy ways." The Hebrew word for "keep" — shamar — means to guard, to watch, to preserve. This is active, assigned, specific oversight — not general goodwill. The child who is ill is under the same charge.
Commentary is from a charismatic Protestant perspective, drawing on KJV text and public-domain sources including Spurgeon, Andrew Murray, and Matthew Henry.