Isaiah 46:4 addresses the specific anxiety of old age with extraordinary directness: "even to your old age I am he; and even to hoar hairs will I carry you: I have made, and I will bear; even I will carry, and will deliver you." The Hebrew nasa — 'carry' — is used for physical carrying, as you would carry a person who cannot walk. God does not retire from caring for his people when they reach retirement age. He describes carrying them through old age as something he will personally do.
Psalm 71 is believed to be a psalm written in old age — verse 9 says "Cast me not off in the time of old age; forsake me not when my strength faileth," and verse 18 says "Now also when I am old and greyheaded, O God, forsake me not." The fears named in this psalm are the specific fears of old age: abandonment, fading strength, vulnerability. The psalm names them as legitimate prayers and brings them to God.
Commentary is from a charismatic Protestant perspective, drawing on KJV text and public-domain sources including Spurgeon, Andrew Murray, and Matthew Henry.