Why did Jesus write for a second time on the ground in Jn 8: 1-8?

We are not told what Jesus wrote, only that he wrote it in the dust (or ground, as it varies by translation), so it is the dust that is important. Ashes to ashes, dust to dust... To return to dust is to die and is a common metaphor in the Bible.

The accusers had only one goal for this woman, to return her to dust. She was a subject of their judgment and their concern for her would end with her death.

Jesus desired more for this woman than judgment. He wished to make her righteous. He commanded her to repent from her sin and gave her the possibility to do so by sparing her life. Thus there are two uses of dust. The first is the just judgment we all are subject to, to return to dust. The second is for that dust to be reanimated at the time of the resurrection of the just. Jesus is the resurrection and the life.

Two is the symbolic number for the Christ. Two natures: divine and human. The Word in two testaments, old and new. Two comings, at the incarnation and at the end of history.

Jesus talked about the ground, the soil, in another way, in his parable of the four soils. The success or failure of the crop had something to do with the quality of the soil. The tone is one of responsibility. Did you do what you could to keep that seed alive and growing? However, two things we cannot do. Those things are God's. The first is plowing. The second is planting.

Plowing is the training we receive through personal suffering, superintended by God. The breaking of the soil softens our hearts and removes some of the stones.

Planting is the insertion of the seed. The seed is the gospel of Christ. We didn't invent it. It comes from outside of us. All we are to do is cooperate with its growth in us. What it will become is tied up in the nature of that seed.

Jesus writes upon the dirt twice. It makes sense that the first time corresponds to plowing, the suffering of sin and consequence of being subject to death by stoning. That is the woman's wakeup call. The second time Jesus writes corresponds to the planting of the seed of righteousness and forgiveness, the love of Christ.

For that woman, there was more to write in that dirt, but it would now be up to her to write it with the actions she would take after she walked away.

Firstly, lets be clear the accusers were ready to kill, breaking that mindset wouldn't have been instant.

The "writing on the wall" was used to issue judgement and had a profound effect on the King of Babylon,

Daniel 5:

⁵ Suddenly the fingers of a human hand appeared and wrote on the plaster of the wall, near the lampstand in the royal palace. The king watched the hand as it wrote. 6 His face turned pale and he was so frightened that his legs became weak and his knees were knocking.

²⁵ “This is the inscription that was written: mene, mene, tekel, parsin

The Babylonian king didn't understand the writing but was nevertheless terrified.

This seems more like the 'writing on the floor'. I would suggest the second written statement was make to sure the message hit home. For example, "Unless you repent you too ..." Luke 13:3-5 was issued twice to make clear its importance.

Jesus could have written something concerning the accusers own sin which would have alarmed them. It could have been the Law (@NigelJ's point). Whatever the case when Jesus said "He who is without sin ...", and reinforced the written message, the accusers would have realised from the writing on the floor they were as guilty of judgement as the adulteress.

The woman was guilty of sin, everyone knew it (caught in the act). The point, however, was all of us are sinners. Most likely Christ wrote the 10 commandments (finger of God).

Let him who is without sin cast the first stone. They all departed, knowing they too were sinners.

As Paul would reiterate, the Law is to convict all of us of our sin.

What then? are we better than they? No, in no wise: for we have before proved both Jews and Gentiles, that they are all under sin; Rom 3:9

What did Christ most likely write the second time? The solution to our sin. The suffering servant of Isaiah 53 is perhaps what He wrote.

He shall see of the travail of his soul, and shall be satisfied: by his knowledge shall my righteous servant justify many; for he shall bear their iniquities. Is 53:11

From a Catholic Church POV, allusion from John 8 is made to Jeremiah 17:13.

O LORD, the hope of Israel, all that forsake thee shall be ashamed, and they that depart from me shall be written in the earth, because they have forsaken the LORD, the fountain of living waters. Jer 17:13

EDIT TO ADD:

Like Moses who received the 10 Commandments twice (Ex 31:18, 34:1), it may be that Christ simply wrote the 10 Commandments twice.

Leviticus 20:10 NASB95 — ‘If there is a man who commits adultery with another man’s wife, one who commits adultery with his friend’s wife, the adulterer and the adulteress shall surely be put to death

Could it be that He wrote first:

the adulteress shall surely be put to death

And then followed it with:

If there is a man who commits adultery with another man’s wife, one who commits adultery with his friend’s wife, the adulterer and...

If they caught a woman in adultery(the adulteress), did they not catch the adulterer as well? Why is only the woman being charged? By withholding the adulterer and judging the adulteress, the law is being disregarded and all of her accusers stand guilty.

I would think all Christian traditions will admit that the real answer will ultimately remain elusive. All we can do is speculate, as the 3 answers also show. Protestant GotQuestions article offers more speculation: What was Jesus writing in the dirt/sand when the Pharisees brought to Him a woman caught in adultery?.

But since you're asking an answer from a Catholic scholar, I hope this blog article by Catholic priest, author, and speaker Fr. Dwight Longenecker can give you the best answer: Why did Jesus write with his finger in the dust?

After discarding his own (Jesus performing a prophetic action referring to himself as "the finger of God", Luke 11:19-20, similar to NigelJ's comment), he offered 3 traditional interpretations and think that the 3rd one is the correct one:

1. Jesus was stalling for time.

2. Jesus was writing the names and sins of the accusers in the dust, an interpretation since St. Jerome.

3. Jesus wrote his accusers' names in the dust as prophetic sign referring to Jer 17:13. This interpretation is by St. Augustine. The context for this is John 7, esp. John 7:38

   Whoever believes in me, as Scripture has said, rivers of living water will flow from within them.

   But who is the "Spring of living Water"? The answer is in Jer 17:13:

   Lord, you are the hope of Israel; all who forsake you will be put to shame. Those who turn away from you will be written in the dust because they have forsaken the Lord, the spring of living water.

   Fr. Longnecker concluded:

   So the writing in the dust is one of Jesus’ signs to show who he really is. He is the Lord, the Spring of Living Water. If you reject him your name will be written in the dust of destiny.

For more on this interpretation, see Catholic professor of Sacred Scripture Dr. Brant Pitre (who wrote many books on the Jewish background of the New Testament) explains in this short 8 minute video What did Jesus Write in the Sand? According to Dr. Pitre, John tells us that Jesus did it twice for emphasis, a literary convention.