Will God, through the Holy Spirit, finally give up on calling someone for salvation, if the person continues to reject the call?

I have heard much of my life of the danger of sinning away our day of grace. This idea is that the Holy Spirit will only work in our hearts for so long, but at some time will cease and we are at that time, even if still alive, condemned to hell.

We know that the Holy Spirit convicts a man and draws him to Christ (John 16:8-11 [8] And when he is come, he will reprove the world of sin, and of righteousness, and of judgment: [9] Of sin, because they believe not on me; [10] Of righteousness, because I go to my Father, and ye see me no more; [11] Of judgment, because the prince of this world is judged.
See All...). It is the work of the Spirit to testify of the Son (John 15:26But when the Comforter is come, whom I will send unto you from the Father, even the Spirit of truth, which proceedeth from the Father, he shall testify of me:
See All...) and glorify Him (John 16:14He shall glorify me: for he shall receive of mine, and shall shew it unto you.
See All...). Also, the natural man (lost man) cannot understand spiritual things without the teaching ministry of the Holy Spirit (1 Corinthians 2:13-14 [13] Which things also we speak, not in the words which man's wisdom teacheth, but which the Holy Ghost teacheth; comparing spiritual things with spiritual. [14] But the natural man receiveth not the things of the Spirit of God: for they are foolishness unto him: neither can he know them, because they are spiritually discerned.
See All...). Jesus states in John 6:44No man can come to me, except the Father which hath sent me draw him: and I will raise him up at the last day.
See All..., "No man can come to me, except the Father which hath sent me draw him: and I will raise him up at the last day." However, in further explanation of this, Jesus says of His crucifixion, "And I, if I be lifted up from the earth, will draw all men unto me" (John 12:32And I, if I be lifted up from the earth, will draw all men unto me.
See All...). So, we see that Jesus draws all men to Himself through His death on the cross.

The above paragraph deals with the importance of the drawing of the Spirit for salvation. Those who teach that some men reach a time when the Spirit will no longer draw them will often use Genesis 6:3And the LORD said, My spirit shall not always strive with man, for that he also is flesh: yet his days shall be an hundred and twenty years.
See All..., which states, "And the LORD said, My spirit shall not always strive with man, for that he also is flesh: yet his days shall be an hundred and twenty years." God declares that His Spirit will not always strive with man. But, before we make this refer to a refusal to deal with the living, we need to understand the context. This refers to the time before the flood. The verse says that man has another 120 years before he will be cut off. What happened then? The answer is that the flood came and killed all the people who were not in the ark. So, what was the point at which the Spirit ceased to strive with man? It was at the time of his death. That does not support the idea of which we speak.

Practical experience supports the idea that conviction is not always working the same way in a man and that there may be times when the conviction and therefore the drawing of the Spirit is so absent that there seems to be no readiness to be saved or any interest in the matter. I believe scripture can be used to support this idea. But I also believe that man can continue to resist the working of the Spirit to the very end. Stephen told the Jewish council, "Ye stiffnecked and uncircumcised in heart and ears, ye do always resist the Holy Ghost: as your fathers did, so do ye" (Acts 7:51Ye stiffnecked and uncircumcised in heart and ears, ye do always resist the Holy Ghost: as your fathers did, so do ye.
See All...). Yet, if they were resisting Him, was He not still convicting them? There is no need to resist that which has no draw of any sort upon you. Therefore, the Holy Spirit was continuing to convict these Jews even though they constantly and continually resisted Him.

Therefore, to say that some men sin away their day of grace may be creating a doctrine not found in the Bible. At least I have not been able to find it at this time. Even at the time of the flood, the time that the Spirit no longer strove with man was the time that God took them away in death and judgment. That is true today. The deadline clearly defined by the Bible is death. Hebrews 9:27And as it is appointed unto men once to die, but after this the judgment:
See All... states, "And as it is appointed unto men once to die, but after this the judgment." God states that death is the deadline that when crossed leads to certain judgment. On the other hand, the Bible refers specifically to God's patience in giving men time to repent. He is "longsuffering to us-ward, not willing that any should perish, but that all should come to repentance" (2 Peter 3:9The Lord is not slack concerning his promise, as some men count slackness; but is longsuffering to us-ward, not willing that any should perish, but that all should come to repentance.
See All...).

I think the best policy is to consider every man a potential resident of heaven until death makes his destiny certain in one place or the other. Perhaps, even if the Spirit has ceased to deal with a soul because of that person's resistance--perhaps He would deal with them again because we plead with Him for the sake of that soul. God is one who "will have all men to be saved, and to come unto the knowledge of the truth" (1 Timothy 2:4Who will have all men to be saved, and to come unto the knowledge of the truth.
See All...). That means that His desired will for all men is that they might be saved. That is why He sent His Son to die and pay for their sins. That is why He sent the Spirit to draw them to Himself. According to Romans 2:4Or despisest thou the riches of his goodness and forbearance and longsuffering; not knowing that the goodness of God leadeth thee to repentance?
See All..., it is the goodness of God as seen in His forbearance and longsuffering that leads man to repentance. We should never sell this forbearance short. Neither should we ever count a soul down that is not out.