Has anyone had a baby who died during the delivery?

My mother, about 30+ years ago lost her first child as she was in labor at the hospital. She can only remember bits and pieces, and being labor and being at the hospital. The first time the nurses checked the baby's heart rate it was fine, the next time they went to check on it the baby was dead. I'm 5 months preganant and I know I will be petrified at the hospital. Can anyone tell me sources of information on the statistics on this, or else if it happened to you? No she never found out what happened because she was too upset at the time to deal with it. My mum now says she was way overdue (by like 3 or more weeks) at delivery but the doctor wouldn't listen to her