Carter loses his son in the fifth month of pregnancy
aired in 2005 (?)
Ginny loses her daughter in the fifth month of pregnancy. Terrible example of pregnancy loss. They do address the issue of grief well. But they don't address the delivery at all or the reason for the loss.
Lucy loses her twin sons. This is discussed cryptically. They don't talk about why, but the show does a good job of showing her grief process throughout the season.
Primetime Special: 2006
"Where the Boys Are" first aired November 2006
A patient falls and her baby dies. Dr. Addison Shephard helps deliver the baby still.
This is the most realistic depiction I have seen on television so far.
If you know of other television shows please email them to me so I can add them to this list.