Huh! Is that a Apple bug or a RunKeeper bug. You do know Apple is not writing third party apps don't you? If the info is collected by Apple and then RunKeeper is just looking it up... Well, thaT's different, but that's not how RunKeeper used to work last time I checked. If it is an app bug, maybe you should try filing it with the App maker.
The Shutdown thing seems to be a battery calibration thing (often fixed by draining the battery completely). If the phone is near zero, it can power on, but then any use (phone call coming it, App), will use enough juice to shut it down again. That happens even if the battery is not really at the value it is reporting. Had the same issue, mine shut down at 25% (it was in fact at 0) and I could charge it over 100% (it only showed at 100% though); when over 100% it often took more than an hour to get under 100% even when browsing on 3G.
So, in fact, it isn't shutting down before its at zero, it is just not reporting the correct number.