PCs Don't Stay Asleep

I have a couple computers running Windows 7 Pro which I access with TeamViewer from time to time. I went through some trouble to get them to respond to Wake On Lan requests, as part of my intention to  have them sleep most of the time for the sake of power saving. But, these computers refuse to stay asleep. Their sleep settings have them set to go to sleep after an hour and I believe they obey this but after approximately a minute they both wake back up. 

I have done research on why a Windows 7 PC would refuse to stay asleep, and it has yielded no answer. I'm wondering if it could be because of TeamViewer and/or Wake on Lan.