Hi,
I have an iPhone 4 that has worked like a charm for about a year. Since upgrading to 5.0.1 I believe it randomly shuts off, but so far always in my pocket. I've tried all sorts of covers---no difference. I can't see how pressing buttons inadvertently can turn it off, anyway (except for simultaneous 15 sec home+off). I don't think the being in the pocket is relevant, but it is a remarkable correlation.
Strange behavior after turning on again:
- I do not have to unlock the Sim card
- I do not have battery usage statistics in settings-> general -> usage -> usage. Just a dash (a proper one, an en-dash---this is apple after all:-) even though I have fully charged it many times.
These two point suggest---for me---it is a software issue.
Cheers,