I've noticed on a number of Android phones that it tends to get laggy or could even shut down randomly at low battery levels if there is a number of processes running.
I am wondering if the case is you having very low battery levels, but there are a number of processes running in the background. Note that pressing the home button to exit an application will NOT turn off that app. It merely sends the app to the background. To exit an app, either press "back" button or menu>exit. If an app does not have an exit button or back does not completely exit it, it means its a normal background running service anyway, and the OS will turn it off on its own if not accessed after a certain amount of time, or when resources are needed.