This isn't as easy a question to answer as you might think, and the reason is because the Bible indicates that God both gives up on us -- and He doesn't! Let me explain.
On one hand, at times God seemingly gives up on us and leaves us alone, allowing us to go our own way and not stopping us, even when we're headed toward disaster. This happens, the Bible says, when our sin and stubbornness become so great that we refuse to listen to Him, no matter how often He warns us. Then, the Bible says, we end up paying the price for our sins -- and God lets it happen. The Bible says, "God gave them up" (Romans 1:26, NKJV).
But on the other hand, God is always ready to forgive us and save us, no matter how far we've drifted away from Him. We may turn our backs on someone who's offended us and refuse to have anything more to do with them -- but God never does. No matter how far we've fallen, God still loves us and yearns for us to be with Him in heaven forever.
Don't risk your soul; don't turn your back on God. Instead, thank Him for sending His only Son, Jesus Christ, into the world to save you, and invite Him into your life today. The Bible says, "For God did not send his Son into the world to condemn the world, but to save the world through him" (John 3:17).