7 mentions of night in Gospel of John From reading Job 35:10 and Ps. 77:6 we understand that night is used to represent trials, a period of distress, trouble.

Then, in the Gospel of John, we can read 7 mentions of night, starting from when Nicodemus comes to Jesus (John 3).

What can we infer from this?
Well spotted.  I think you are onto something here.  The number seven is popular in John's Gospel.  There are seven signs, seven "I am" sayings, the woman at the well had five husbands plus one who was not her husband, so the One sitting at the well waiting for her is her seventh Husband, the Seventh Man in her life, her perfect Man and Husband.

This will only go so far, to encourage more thought on the question.

First off, note how the Gospel of John begins with Jesus being "the light":


  In him was life, and the life was the light of men.  The light shines in the darkness and the darkness has not overcome it (John 1:4, 5).


and


  The true light that enlightens every man was coming into the world, (John 1:9).


Now for the occurrences:-


Nicodemus ... "the same came to Jesus by night" (John 3:2)
Nicodemus says unto them (he that came to Jesus by night, being one of them) (John 7:50) 
Jesus speaking ... "the night comes, when no man can work"  (John 9:4)
Jesus speaking ... "but if a man walk in the night, he stumbles, because there is no light in him" (John 11:10)
Judas Iscariot .. "having received the sop went immediately out: and it was night" (John 13:30)
"There came also Nicodemus, which at the first came to Jesus by night, and brought a mixture of myrrh and aloes, about a hundred pound weight" (John 19:39).
the disciples go fishing... "and that night they caught nothing" (John 21:3)


However, first note that there are seven occurrences of "night" in the Greek Received Text upon which the KJV and NKJV are based, but only six occurrences in the Greek "Revised Version" upon which most modern versions are based.  The difference is that the Greek for "night" does not appear in John 7:50 in the Greek "Revised Version".  So, eg, John 7:50 in the Revised Standard Version has translated the Greek to "Nicodemus, who had gone to him before, and who was one of them, said to them...".

With Nicodemus his first coming to Jesus was in darkness, both literally, because it was night, and spiritually because he couldn't see very much spiritual truth; he knew nothing about the new birth, he did not know that faith in Christ is what he needed.  Nicodemus was clever, well educated, knowledgeable in the Old Testament Scriptures, and even a teacher of those Scriptures - but none of these things brought him any light: only faith in Jesus can do this.  

The subsequent mentions of Nicodemus show a progressive growth in love for Jesus; first he is willing to come and talk with Jesus, but only secretly at night, then he is willing to stand up for Jesus amongst his fellow religious leaders (John 7:50), and last he demonstrates a clear love for Jesus (John 19:39).  A little biographical sketch of a sinner, Nicodemus, and his progress from very great spiritual darkness into spiritual light is embedded in and throughout John's Gospel.  We must not expect people to go from darkness to light the moment they hear the gospel; we must pray for unbelievers with perseverance.  First the seed of the Word is planted in the heart, then that seed begins to grow secretly in the heart, and finally it brings forth the fruit which is plain to see.

The other mentions of "night" all carry negative or very negative connotations:  "no man can work"; "if a man walk in the night, he stumbles"; Judas Iscariot's betrayal; they caught no fish.

So, perhaps, if we do not have the Light of the World, if we do not believe on him as Nicodemus came to do we will not be able to work; we will stumble, we will betray Jesus, we will not bear any fruit.  There being seven occurrences of the word "night", maybe we could preach it since it implies that, if we do not have all our hope in Christ and Him crucified, we will fail in all these respects on Mondays, Tuesdays, Wednesdays, Thursdays, etc... ie every day of the week, all the days of our lives. The life of an unbeliever is a continual walking in darkness, and that darkness is very great.

But if we believe on Him who is the Light of the World then we will never stumble, we will always be working for Him, never betray Him, and always bearing fruit.