Many times their closest connections are with the missionaries who introduced them to the gospel. But Mormon missionaries come and go. If we members aren't more open and receptive, we will find many new converts falling away after their missionaries are gone.
As more "seasoned" members of the church, we need to learn how to be a good friend to new converts. I'd like to offer a few suggestions from my own personal experiences.
1. Step out of your comfort zone. I consider myself somewhat shy around people I don't know, but I make sure that if there is a new face among the congregation I take the time to introduce myself to them. I know how it feels to be the new person. I know how it good it feels to have someone acknowledge you and try to make you feel comfortable. So if you notice a new face in your ward, don't just stare. Go up and introduce yourself.