The same Greek word translated reprobate in the KJV Bible (adokimos, Strong's Concordance Number #G96) is translated as depraved in the NIV version of Romans 1:28, disapproved in the NKJV version of 2Timothy 3:8 and worthless in the NASB version of Titus 1:16.
What do we know about someone who has this kind of mind? We know from Romans 1:28 that the people under discussion did not like to retain God in their knowledge. As a result, God gave them over to this depraved, disapproved and virtually worthless state of mind.
The people Paul is discussing in Romans chapter one are godless and wicked men who suppress the truth by their wickedness (Romans 1:18). Paul states regarding these men:
"For since the creation of the world His invisible attributes are clearly seen, being understood by the things that are made, even His eternal power and Godhead, so that they are without excuse, because, although they knew God, they did not glorify Him as God, nor were thankful, but became futile in their thoughts, and their foolish hearts were darkened.
"Professing to be wise, they became fools, and changed the glory of the incorruptible God into an image made like corruptible man — and birds and four-footed animals and creeping things." (Romans 1:20-23, NKJV)
Paul is railing against some vile people who crept into the early church and began to teach other things, other doctrines, other gospels, and were successful at leading many astray. It was a problem right from the start, and it has continued to be a problem down to this very day! Perhaps as we continue reading what Paul said in Romans chapter one, we might recognize some people or organizations in the news today!
We know some of the early heresies of the first century church. Among the leading heresies was Gnosticism, from "gnosis" (knowledge). These liars taught a special kind of "inside knowledge" that led many away from the truth they had recently learned from the apostles! May I recommend reading the article Was Jesus the REAL source of Christianity?
Many of the epistles are written as a direct defense of "the faith which was once for all delivered to the saints." (Jude 3, NKJV) against the onslaught of Gnosticism and other heresies. Paul wasn't pulling any punches when he railed against these enemies of the truth, whether you're reading about it in Romans or any of his other epistles. Paul was very concerned about the danger these snakes could do to the church members. He rightly called them depraved, debased, and ultimately, rejected!
What about you and me? Might we have a reprobate mind? The good news is, truly converted followers of our Lord and Savior Jesus Christ don't have to worry about such a thing.