According to the findings of several reports of iPhone users, it would seem that iOS 10.1.1 may cause excessive battery drops and sudden shutdowns of devices.
Apple released iOS 10.1.1 to fix a bug related to the app but the Health update, although it is always recommended to upgrade a device to the latest version, it seems to have brought more problems than they wanted to fix. Many users then complain about the battery excessive drops and, in several cases, the sudden shutdowns of the iPhone.
Expect a new update able to correct these problems. We will update you as soon as we know more on the subject.