Upon buying my Captivate, that night I did my initial charge of the battery, after which my phone turned off every time the screen turned off. This, by the way, seems to be the point that this problem usually shows up after the first battery charge. I tried all the suggestions here and else where over the first weekend. Called Radio Shack on Monday and the woman who sold me the phone said 'Captivates just do that.' Called AT&T, they had never heard of the problem, of course. Though they strongly suggested not returning it to the store for a replacement but sending it to Samsung for repair.
Samsung also had never heard of this problem before my call. (even though it is the second most often asked question on their site) They did issue me an RMA, e-mailed me a shipping label and instructions for shipping and I was told turn around time would be 6 days and that the phone would be fixed.
Exactly 6 days later the phone was back in my hands and has worked perfectly ever since. (so much for the software band aids)