55 years after the events? Try again.
But you ask a couple of good questions. A big part of the answer is that the Apostles were working every waking moment to spread the Gospel. Paul was the Apostle to the Gentiles and the rest were Apostles to the Jews. Paul's letters (Epistles) were often written as follow-ups to churches he had planted years before.
Frankly, between full-time ministry and frequent hardships it's a miracle :) that any of the New Testament was written as soon as it was.
As for writing about Jesus while He was alive, His followers were only disciples (students) during the last three-years of His life. After His crucifixion, they were cowering in fear of the authorities until Jesus showed Himself to them three days later. It was only after they were convinced of His resurrection, witnessed His ascension, and were empowered by the Holy Spirit that they became bold enough to begin their own ministries in the face of constant persecution.
Ron Paul - Honorary Founding Father