The short answer to this is: no — grace doesn’t run out. However, this doesn't mean we are given a free pass to sin. We are directly told not to in Romans 6:1–6. There we are told that we shall not continue in sin so that grace may abound. We are also shown that, through grace, we are partakers of the death and resurrection of Christ, which means our sinful body is put to death — that is to say, our sinful way of life is no more, and we no longer live to serve sin but instead walk in the likeness of Christ. In Romans 6:16–18 we are instructed that we are the servants of whom we obey, which is to say we can’t walk in sin and think that we are still serving the Lord. But if we truly have chosen to obey the Lord, we will turn away from sin; we will be his servants and receive the gift of righteousness and holiness.

To return to our opening question of “does grace run out?”—while the answer is no, there is a caveat: there is a window of opportunity for us to accept grace. As the Word says in 1 Thessalonians 5:2–4, the Lord will come as a thief in the night, which is to say he will come when we do not expect him; therefore we are to walk in the light of the Lord so that we won’t be overtaken by darkness on the day of his return but instead will be taken up into the kingdom with the Father.