You are correct Katydid!- They do not come home to visit during their mission- that is part of the point, as well as minimal communication home. They are supposed to be focusing on what they are there to do.
Here is a recent example. Rebecca Lockhart, the first woman to be Utah's House Speaker was dying. Her son was serving a mission in Virginia and did not return home to be at his mother's side. Good for him to be so focused on his religion.
Snip:
"While most of the family was able to be at Lockhart's bedside, her son, Stephen, is currently serving a mission for The Church of Jesus Christ of Latter-day Saints in Richmond, Va. His last goodbye to his mother was on speakerphone, and she couldn't answer back."
http://www.ksl.com/?nid=148&sid=33150890