No, God never gives up on us or refuses to keep trying to draw us to Himself, even when we've turned our backs on Him throughout our lives. The Bible says, "He is patient with you, not wanting anyone to perish, but everyone to come to repentance" (2 Peter 3:9).
At the same time, it's unusual for an older person who has repeatedly turned away from God to turn to Christ as their life nears its end. Why is this? The problem isn't with God, but with them. Over the years, they've grown so hardened toward God that now they can barely hear His voice. Just as your hand grows calloused and insensitive from repeatedly rubbing against the handle of a tool, so our hearts can grow calloused and insensitive to God from repeatedly refusing to listen to Him.
This is why it's dangerous to turn away from God or say that we'll give our lives to Christ later. "Later" may never come, and then we'll find ourselves entering eternity without hope. The Bible warns, "A man who remains stiff-necked after many rebukes will suddenly be destroyed--without remedy" (Proverbs 29:1).
Don't let this happen to you, but turn to Jesus Christ in repentance and faith, and open your heart and life to Him. I've never met a person who regretted giving their life to Jesus -- and neither will you.