Reprobate, Castaway, Rejected
ἀδόκιμος, -ον, (δόκιμος) [from Euripides down], not standing the test, not approved;
Romans 1:28 And even as they did not like to retain God in their knowledge, God gave them over to a reprobate G96 mind, to do those things which are not convenient;
According to the context this word is to "ungodliness and unrighteousness of men, who hold the truth in unrighteousness;". We should not think of unbelievers as those who are "holding down the truth in unrighteousness". Often unbelievers don't want anything to do with the Bible or religion. No, those who teach it is OK for the church to be ungodly and unrighteous and when anyone tries to point out where the New Testament says that is not true they try to hold that down. Many of the "translations" of the Bible have the agenda of holding down the truth of one doctrine or another. Think about the Jehovah's Witness with their translation of the Bible. According to the context these are the ones who are given up to a reprobate mind.
1 Corinthians 9:27 But I keep under my body, and bring it into subjection: lest that by any means, when I have preached to others, I myself should be a castaway. G96
The word castaway is the same word as reprobate, but they translated it this way because Paul is using the example of the Israelites that were castaway in the wilderness. The word is crystal clear, even someone like Paul who had received a heavenly vision, experienced a miracle of having his eyes opened and who preached the word, leading others to salvation. Even he could become a castaway. That doesn't mean he would go to hell. The entire Once Saved Always Saved doctrine is way too simplistic. Yes, Paul is saved from hell, he has the full assurance of that salvation. But even so he can become a castaway. This is like being cut from the team. Imagine you are on an NFL team, and the coach calls you into the office to let you know that you have been cut. So you tell hime "we are all sinners". OK, but you he is looking for 40 that could stand the test and you were not one of them.
2 Corinthians 13:5 Examine yourselves, whether ye be in the faith; prove your own selves. Know ye not your own selves, how that Jesus Christ is in you, except ye be reprobates? G96
The context of this verse is
"we also are weak in him, but we shall live with him by the power of God toward you". Are you living with the power of God operating in you? Yes, we are all weak, but that is not an excuse to live in sin, to live as a slave of sin. The way I look at it we are all like a leaky tire on a car. Initially the holes might be terrible and so you have to spend a lot of time praying and repenting and patching holes. But later you never actually get the tire to be fully patched. Now it has a slow leak, so every day you must fill the tire with air. Every day you are in the word, in prayer, in worship so that you are full of the pneuma, the Holy Spirit. Because you do that you can operate in the power of God. If you go two days without doing that it becomes clear you are flat and that can result in that tire getting a much worse hole in it.
2Timothy 3:8 Now as Jannes and Jambres withstood Moses, so do these also resist the truth: men of corrupt minds, reprobate G96 concerning the faith.
Jannes and Jambres were not Israelites, they were Egyptian "magicians". I would liken them to FreeMasons who infiltrate the church and push this agenda to make the church ungodly and unrighteous. They resist the truth which is another way of saying they try to hold down the truth in unrighteousness.
Titus 1:16 They profess that they know God; but in works they deny him, being abominable, and disobedient, and unto every good work reprobate. G96
We are supposed to judge a tree by its fruit. We are not supposed to take every single ministry that claims to be speaking Jesus Christ without trying and testing it. This is a good example of how some profess to know God, but by their works, their fruit, they deny him. Are we saved by works? No. But, faith is a seed and if it grows it will bear fruit. That fruit is evidence of the faith. Look at Transgender story hour from the pulpit of a church, that is abominable and it is disobedient. Now these ones may have a whole bunch of good works, think of the Shriners, they are a wing of the Freemasons. But they do good works as a cover or disguise, it is like the Mafia donating money to the church to help with their Public Relations.
Hebrews 6:8 But that which beareth thorns and briers is rejected, G96 and is nigh unto cursing; whose end is to be burned.
This word rejected is the same word translated reprobate and castaway. I have heard some teach that Hebrews is a book written to the Jews and is not for Christians. Hebrews is part of the New Testament. That is our covenant with God as a result of Jesus' blood. The word means "river crosser". As Christians when we were baptized we also became "river crossers". If you want to be raptured you will have to be a river crosser, a Hebrew. Abraham was called a Hebrew because he crossed the river to enter into the good land. He is the father of faith, if you are a child of Abraham then you are a river crosser and the book of Hebrews is written for you. When someone teaches that a verse in the New Testament or even an entire book like Hebrews or James is not for Christians, that is what Paul meant by "holding down the truth in unrighteousness" and "they also resist the truth".