There seems to be a special bond between Paul and Timothy that is something that I have observed many times in real life. We had a friend in Denver that had a spiritual daughter that drove half way across the US to see them for a few days. The chances are good that Timothy was saved on Paul's first missionary journey because on the second journey Timothy is already saved. It is also noteworthy in Acts 16 that Paul had been discipling Timothy as well. Paul took Timothy with him on some of his journeys.
Discipleship is of great importance after salvation.
The concept is similar to giving natural birth to a baby and leaving the infant to fend for itself in the world. Today when a mother abandons a newborn the world is horrified - even in our callous society. When you assist in the spiritual birth of a believer it should be your first priority to assure their discipleship. Either do it yourself, or assure that they are founded in a good local church where they will receive the training they need. These seem to be items that Paul was hoping that God would give to Timothy.