I've had every Kindle and every Nook and most Sonys. Neither has died. Of course, the only ones heavily used have been the Kindles and Nooks.
Also been fortunate to never get any of the issues people run into. Only thing I've seen is that the Kindle 3 keyboard keys started getting rubbed off.
The most stable/sturdy ones to me seem
Kindle 3 (the one they now call Kindle Keyboard).
Nook Color (of course, you could argue it's not strictly an 'ereader').