Hi,
I am having a similar problem. I've had the phone for about four months and in the last month it has started randomly turning off and sometimes back on but not always. Several times I have taken it our of my pocket and found it asking for the SIM PIN (ie it has turned off then back on).
At first I thought it was when battery was low, then I caught it turning off with > 80% batt.
I also thought maybe the power button got pressed in my pocket but then it did its trick while sitting on the desk.
I found a thread complaining about similar behaviour on the Galaxy S (AT&T) forum but no solutions except 'exchange the phone'. I would have no confidence in the exchanging option as this problem has taken 3 months to surface in my case and longer in other people's.
I have also seen the real short screen timeout problem mentioned by OP.
This problem is getting close to making the phone unusable - turned off at least 5 times today! Turned back on on 4 of those occasions.
I have Juice Defender loaded but have tried disabling it and problem persists. Maybe I need to uninstall JD?
Comments/Suggestions?
DG