I've been through some awful situations. It's affected my mental health. In addition I had a child years ago and I think similar things happened to them too.
Last night, again, I lost my temper . I'm not sure God's Spirit is with me still.
When is it time to simply acknowledge that I can't be a believer?
ClearPerspective, your question counters your self identification as a skeptic. Not knowing whether you're a believer struggling with character issues or a non-believer seeking a confident faith, let me offer this response:
First, consider what your faith is based on. Is it real world evidence or your behavior? In the case for Christianity, it's truth rests upon scientific, archaeological, historical, prophetic, and manuscript authority evidence. That truth, by the way, exists regardless of whether you believe it or how you respond to it.
Unlike other religions in the world, a Christian is saved by faith in Christ alone. The character changes come afterwards as fruits of the Spirit, and this is a life long process of imperfection that most of us struggle with.
To answer your question directly, I'd say no person should ever accept being a non-believer in God. A mere look into the night sky clearly reveals his existence and glory, as does the world and complexity of life around us. And if he created the universe and all life as we know it, he must have had a reason - a purpose for our life and a desire to connect with his creation. The rational question then becomes what religion leads to the right relationship with God?
If you study God and the Bible from Christian apologetic sources, you'll find reasons for the faith that build a strong foundation for belief. With that, it only takes a receptive heart to accept the truth, invite the Holy Spirit into your heart, and be truly saved for all eternity. With that foundation, your Christian walk afterwards will progress, but don't let your performance or setbacks undermine what you've learned to be true and accepted in your heart.
I think, if you work on grounding your faith better, you'll find your heart and character changes follow naturally.