I have an iPhone 3Gs 16GB running iOS 5.1.1 build 9B206. (my daughter has one as well and is having the same issues.)
Since the upgrade to iOS 5 we have experienced the phone being shut down (crashes) while using them. At first I thought it was due to low battery, but it does it at full charges as well. It does it more specifically with apps that use a lot of memory (or refreshing of information online), such as maps, weather, facebook, etc.
Anyone else having this trouble? Should I revert to an earlier iOS?