There was a study published in the British Medical Journal about sleep and stillbirth. One hundred and fifty five womean that were at least 28 weeks pregnant were asked questions about sleep position, sleep duration, time of day they sleep, snoring, daytime sleepiness, and urinating at night.
The results show that the risk of still birth is higher when pregnant women sleep on their back or right side, compared to their left side. The researchers think that on the back or right side, blood flow to the fetus might be reduced. Risk of stillbirth was higher in those pregnant women who slept regularly during the day and who slept longer than average at night. Also, there was higher risk of stillbirth in pregnant women who woke up to empty their bladders less than two times per night. Finally, there was no link between snoring, daytime sleepiness, and risk of stillbirth.
This was a small study and relied on women's self-report. Most people are not aware of how much time they sleep in any position, so these results should be interpreted carefully.