DH just waited two weeks for his replacement unit to show up, for the very issue you mentioned -- it would randomly turn itself off on rides. Very frustrating because he never knew what portion of the ride statistics it would retain once he turned it back on after realizing it was AWOL. He didn't have any issues with Garmin customer service, but then he has a little bit of leverage -- this is the second time he's had to replace a unit, although I don't remember what the first time was for. So, yes, he's actually on his third Edge 305 because you never get yours back, just a refurbished unit.
He's the numbers-driven, data guy, so I understand your anxiety over riding 'naked'. On the other hand, I like having access to the data while I'm riding, but couldn't care less once I'm done. Crunching the numbers doesn't entice me, and I'll often wait to download a week's worth of rides at a time. Ironically, my Edge 305 has been the reliable unit to this point. We often ride together, on the same cruddy chip 'n seal roads, so it's a mystery as to why his unit is cantankerous and mine is well-behaved.
The only issue I've had is that I'll plot/download a course and discover part way through the ride that the virtual training partner has decided to mutiny -- frozen in both time and space, with directions for home locked tightly in its tiny little brain. Gulp! And it only happens on rides over 60 miles. Not the best of circumstances for little ol' directionally challenged me who can ride a road numerous times and still not recognize it the next time I see it...
"If we know where we want to go, then even a stony road is bearable." ~~ Horst Koehler