There are many ideas concerning reprobates. Let me start with two of the theological uses of the term.
According to most accepted theology, a reprobate is one who is condemned to eternal punishment because he is not one of the elect. John Calvin, in his "Institutes of the Christian Religion" (3.23.1) stated: "God is said to set apart those whom he adopts into salvation; it will be highly absurd to say that others acquire by chance or obtain by their own effort what election alone confers on a few. Therefore, those whom God passes over, he condemns; and this he does for no other reason than that he wills to exclude them from the inheritance which he predestines for his own children." This is a doctrine that I reject as unscriptural.
A second teaching concerning reprobates is the one to which you refer. It is the teaching that reprobates are those who have been condemned to hell by the decision of God to no longer allow His Spirit to convict them. However, before we look at Romans 1:28, I would like to consider the word and doctrine according to its use in scripture. This should be our final authority.
Reprobate (or reprobates) is used seven times in the Bible: Jeremiah 6:30; Romans 1:28; 2 Corinthians 13:5, 6, 7; 2 Timothy 3:8; Titus 1:16. It is related to the word reprove. However, reprove is based on the word prove, which means to test. Reprobates then would be those who have been put to the test and are found wanting and so are reproved. In Jeremiah 6:30, men are said to be like reprobate silver because they are rejected. We can see the picture of silver being tested and discovered to be false. Therefore, it is rejected.
But this brings up an interesting idea. The reprobate silver seemed to be silver. It was only after it was tested that it was found to be counterfeit and rejected. This idea continues in other references to reprobates. Paul told the Corinthians to examine themselves to see if they were truly in the faith. He told them, "prove your own selves. Know ye not your own selves, how that Jesus Christ is in you, except ye be reprobates?" (2 Corinthians 13:5). Notice the key word, prove. They were to prove or test themselves. If they were not truly in Christ, then they would be reproved--because they were reprobates.
Therefore we see that a reprobate is one who have been tested (proved) and found lacking; so he is reproved or rejected as a true believer. It must follow that a reprobate claims to be a true follower of God and yet is found false when put to the test. This fits perfectly with Titus 1:16, which states, "They profess that they know God; but in works they deny him, being abominable, and disobedient, and unto every good work reprobate." These men profess to know God but in their works they deny Him. They fail to pass the test of genuine faith. I do not see how this can apply to those who have "sinned away their day of grace." Again, this is not a true biblical doctrine.
Now, we need to look at Romans 1:28. I will admit that this passage could lead many to believe in a rejection by God that includes certain judgment in hell. However, my main point is that rejection by God can be partial now and is not complete until someone dies lost. In Lamentations 5:22, Jeremiah could say, "But thou hast utterly rejected us; thou art very wroth against us." Yet, in the same book he could proclaim, "It is of the LORD'S mercies that we are not consumed, because his compassions fail not" (Lamentations 3:22). Utter rejection was not eternal rejection. They were completely rejected in one sense, but God would still show mercies to them.
Romans, chapter one, deals with a group of people who have turned away from the Lord. These people "changed the glory of the uncorruptible God into an image made like to corruptible man, and to birds, and fourfooted beasts, and creeping things" (Romans 1:23). Because of their wickedness, God turned against them. Three times in the chapter we read that God gave them up in one way or another. First, God "gave them up to uncleanness through the lusts of their own hearts" (Romans 1:24). Second, "God gave them up unto vile affections" (Romans 1:26). Third, we read, "And even as they did not like to retain God in their knowledge, God gave them over to a reprobate mind, to do those things which are not convenient" (Romans 1:28).
The first giving up had to do with their hearts. The second had to do with with their affections or desires. The third had to do with their minds. He did this because they did not like to retain God in their knowledge. Now that is interesting. They had God in their knowledge but did not like to retain Him. But they had changed the glory of God into an image and the truth of God into a lie. They started out with the true God and the truth of God but left it all in order to follow their own lusts. As a result, God gave them up to do those things which were not convenient. He gave them over to the practice and the fruits of their lusts.
It is admittedly clear that these men were turned over to their lusts without the restraining hand of God. However, only if we approach this scripture assuming that they can never get saved after this can we find this teaching in these verses. God no longer restrained them. You see, even the lost are kept from going to the depths their minds can conceive by the gracious restraining of God. However, these people fought Him so much that He gave them over to whatever wickedness their minds could imagine to do. One of the dangers to the human race is that "now nothing will be restrained from them, which they have imagined to do" (Genesis 11:6). It is only God's grace that keeps man from going as far down as he is capable of going.
These men have lost this gracious restraint. God has given them up to their uncleanness and to their vile affections. He has given them over to their reprobate mind. What is this? It is a mind that has been tested and found wanting. It is a mind that is reproved because of its wickedness. And now, this same mind will take them as far as it wants to go. What a terrible fate!
Yet, does God say that this person can from this point never be saved? No. He never states this as a fact or teaches it as a precept. In fact, we have evidence to the contrary. What is mentioned as the ultimate sin of those who have been given up? It is the sin of sodomy. This is the sin that is clearly defined in Romans 1:26-27. It is evidently the lowest depths of this reprobate mind because it is even against the natural state of the lost man. Then, evidently, those who sink into this sin have been given over to their reprobate mind. But can they never be saved? Of course, they can be saved. In 1 Corinthians 6:9-10, Paul defines different categories of the unrighteous. Among those he includes the "effeminate" and "abusers of themselves with mankind." This is a definite reference to sodomites. Then, in the next verse, he states, "And such were some of you: but ye are washed, but ye are sanctified, but ye are justified in the name of the Lord Jesus, and by the Spirit of our God" (1 Corinthians 6:11). Some of these sodomites had gotten saved and had left their sin behind them. Those with a reprobate mind (one that had failed the test and had been reproved) were still able to get saved. Praise the Lord! He is able to save to the uttermost them that come unto God by Him (Hebrews 7:25).