What you say about your uncle's brush with death is undoubtedly true: God preserved his life so he'd have another opportunity to repent and open his heart to Christ. The Bible urges us not to ignore God's warnings, because we won't escape "if we turn away from him who warns us from heaven" (Hebrews 12:25).
Tragically, some people want nothing to do with God. No matter how often He shows His goodness to them, they still refuse to turn to Him. Do you remember Pharaoh in the Old Testament? He cruelly oppressed the Israelites -- but when God told him to free them from their slavery, he refused. Repeatedly, God sent terrible plagues on his land, and at times it seemed like he might relent and set them free. But eventually he refused; the Bible says, "he hardened his heart and would not listen" (Exodus 8:15). It led to his destruction.
Does this mean there is no hope for your uncle? No, it doesn't, because God is able to break through even the most stubborn heart -- which is why prayer is so important. Pray for your uncle, that God will convict him of his sin and convince him of his need to turn to Christ.
In addition, ask God to help you be an example to your uncle -- an example of Christ's love and purity and hope. Remember: Often our lives speak more loudly than our words.