So I'm thinking this almost certainly points to a software problem, rather than hardware.
Depending how much RAM you have 1/2 hour is probably not enough to test the RAM. A RAM test writes and read to every address, which can take ours depending on your system configuration.
Probably, I would still lean toward power management, hibernation to be specific. Is this a laptop?
Also you can check the manufactures website for updates, if it's a laptop look for a BIOS update in particular. All modern processors have built in power stepping that lowers the cpu power during inactivity.
Double check all power options in control panel - power options - change plane settings (under active radio button) - change advanced power settings.
Look for any setting set to around 10 minutes.