It seems (from trying to find a solution myself) that there are many possible causes of this problem, including a whole category of programmes that somehow override or interfere with your power settings. In my case I now believe the culprit to be "Intel Rapid Start Technology", which came pre-installed on my Dell XPS 15 (Windows 8.1). Under settings, the option "Timer" was turned on, which the mouse-over help described as "Enables system to transition to Intel Rapid Start Technology after a period of time in sleep".
I think this is supposed to actually save your session to the hard drive (not sure how this is different from hibernation, other than it happens during sleep and it specifically works for SSD drives), but I suspect that it somehow fails to do so on my machine, and so the result is indistinguishable from a regular shutdown.
I've only just discovered this so I haven't yet had the chance to see whether my problem is actually solved now, but I thought I'd share it while I've still got this page open.