First off, I've had my Captivate 2 weeks... of which I have experienced the random shut-off / non-wake-up from sleep problem exactly 6 times. From those six, 3 have been approx. 15 minutes after unplugging from the "100%" charge notice, and the other 3 have been entirely random. After reading as many posts as possible about this specific issue, I've gathered the information, jotted down what I felt was likely or unlikely, created my tables and deduced a possible solution for my particular phone and specific scenario without changing settings or uninstalling applications or changing roms.
Here are some thoughts, since it seems the workarounds presented are going in every single direction:
Software / App problem: Highly unlikely. ....Owners would be having more of an issue while they are actively using the phone and the apps... not just the specific case of "going to sleep and not waking up".
Power settings: Possible, but there really aren't a whole lot of options to mess with.
Hardware / Phone problem: unlikely. ...It does not appear, from everyone's post, that it happens when plugged in. If it were an internal problem, it would happen whether plugged in or running on battery. Also, the fact that some owners could be on their 2nd or 3rd phone and it still shuts off after sleep is unlikely.
Known scenarios: It seems to happen more after being charged for a longer period of time. It does NOT happen plugged in. There's a HUGE number of posts where owners are getting extremely erratic phone charging characteristics and poor battery life performance. In addition, the battery meter and charge meter are innacurate to many experiencing this problem.
Summary thoughts: The problem with the shut-off AND the erratic charge behavior combined with poor battery performance and new batteries not always fixing the problem points me in one direction... the battery connection itself.
Prior to this fix, my battery performance was underwhelming... not nearly as bad as some have claimed, but not nearly as good as the spec sheets state. Previous numbers were a 2%+ drop per hour standby (nowhere near the 300 hours as per Samsung), and moderate use (flipping through pages, checking out a couple of sites, emailing and texting, etc.) dropped approx. 10% per hour... and heavy use dropped 15-20% per hour. I do not have any numbers for the battery draw for talk time, but I can't imagine it being that much different than surfing the web, watching a few clips, etc. (what I would consider heavy use).... so based on my previous numbers, there would be NO WAY I could achieve the rated near 6 hours of talk time.
I am 98% business user, so wifi is on all the time, push email to 5 accounts, sync always on, bluetooth always on for my earpiece, and various webservices I have to check in on frequently throughout the day. I do not play games on my phone, but I do enjoy tinkering with the settings and flipping through homescreens etc. often.
After this fix, not only have I not experienced any shutdowns, but my phone seems more responsive and my battery life has shot up at least 2 to 3 fold easy. As I write this, my phone has been unplugged for 2 hours 52 minutes, I've read multiple emails, responded to multiple emails, texted back and forth with my daughters about 20 times, made several phone calls and checked Facebook.... and my meter is at 95%. It also stayed at 100% battery level for nearly 1.5 hours, and I no longer jump from 100 to 98% as soon as I unplug the battery. This has been consistent for nearly 4 days now.
Here is my best guess... somewhere along the manufacturing line and shipping, along with storage, there's an extra oxidative film on the terminals to the battery. I do not know if it's on the battery side or the phone side, but something is there... maybe a bad batch of gold terminals, who knows. I imagine the sleep setting uses such a specific and minute amount of energy that any resistance on these terminals causes this phone, and probably many others, to get confused.... just like it does on many cars' electrical sensors (of which the fix was exactly the same BTW on my erratic Jag).
So, turn off your phone, pop out the battery, get a q-tip out and dip it lightly in rubbing alcohol. Carefully rub the three gold connectors to the battery (on the phone side), and also do the three terminals on the battery. AFTER you've done that, take a white pencil eraser and LIGHTLY rub the gold surfaces to remove any oxidation. It doesn't matter if it looks shiny and clean already, we're talking about such a specific low energy requirement, so any resistance can cause havoc.
Let dry, put battery back in, and I would be very surprised if this doesn't fix your shutdown issues and battery life woes if those issues happen to be the same as mine.
TOMTOM HA!!! 
