Think first I would download BatteryInfoView from Nirsoft and check to see if the power consumption goes up quite a bit when projecting. Also I would check the case for hotspots. I have seen HDMI devices that pull more power from the PC than they should.
More technical: open Device Manager and make sure that all of these DPTF and ACPI elements are working properly. The R3/R11 is a ventless design like a tablet and must avoid overheating without a fan. When everything is working propely, it is very reliable but from what you say I am suspecting an overheat issue.
Note in the enclosed picture I have removed things in the middle - from my R3/R11
