Psalm 71:1 In you, O Lord, do I take refuge;
let me never be put to shame!
9 Do not cast me off in the time of old age;
forsake me not when my strength is spent. (ESV)
Apparently he saw that his "time of old age" might be a time of trouble, when he would need God more and more.
As one of Ursula K. Le Guin's fictional characters put it:
But now I have my own question. I never asked questions, I was so busy answering them, but am sixty years old this winter and think I should have time for a question. But it's hard to ask. Here it is. It's like all the time I was working keeping house and raising the kids and making love and earning our keep I thought there was going to come a time or there would be some place where all of it came together. Like it was words I was saying, all my life, all the kinds of work, just a word here and a word there, but finally all the words would make a sentence, and I could read the sentence. I would have made my soul and know what it was for.
But I have made my soul and I don't know what to do with it. Who wants it? I have lived sixty years. All I'll do from now on is the same as what I have done only less of it, while I get weaker and sicker and smaller all the time, shrinking and shrinking around myself, and die. No matter what I did, or made, or know. "Ether, OR," pp. 95-123, in Unlocking the Air and Other Stories (New York: Harper Perennial, 1997). Quote is from p. 108. Originally published in Asimov's, 1995.
To put it more succinctly, but less elegantly, "What has my life been worth?"
James tells us that our lives will be short, and the effect of our life will be temporary:
James 4:13 Come now, you who say, “Today or tomorrow we will go into such and such a town and spend a year there and trade and make a profit”— 14 yet you do not know what tomorrow will bring. What is your life? For you are a mist that appears for a little time and then vanishes. 15 Instead you ought to say, “If the Lord wills, we will live and do this or that.” 16 As it is, you boast in your arrogance. All such boasting is evil. 17 So whoever knows the right thing to do and fails to do it, for him it is sin. (ESV)
No one, no matter what her age, is guaranteed tomorrow. So how shall we live? James tells us, at least partly, in the above passage: Do what is right. That's the best way to live a life worth living, a life that will make a difference, a life that doesn't get smaller and smaller all the time.
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(Added after original post) C. S. Lewis wrote, in The Silver Chair, that there are no accidents. My on-line Bible reading for today, June 10, 2006, included the following: