Hi lily; next time you install an iOS, have a go at the Release Notes. In them, you will find a section in which Apple thanks, by name, iOS contributors whom reported or fixed bugs, developers and so on. There are people out there so savvy that they know the architecture by heart, code by code. Some know power, other GUI etc. Between Apple engineers and all worldwide developers, the odds for the recently named #1 company, with 600 million iPhones active, to have introduced such a bug, is not possible. With the battery issue in the news quite a bit, someone would have found a bug, or if deliberate, someone would have told that already and it would have been the biggest story since the Volkswagen code.
I experienced issues with iOS 9, and clear ones at the 115 cycle mark, 4 months. As Paikinator just told you, if you call Apple Support, speak to a Sr advisor and are that close to the 1 yr mark, you might get a cost free solution.
Here is some examples how installs can affect your phone: one of the iOS installs on this phone gave me a speaker bug, no one hearing me unless I clicked on the External then back to internal or headphones; another gave me an 18 vs 36 hr battery life, be it that I had no heating nor rapid drainage. Another gave me a black screen thing. Each time a reset resolved them. Maybe you just have a random bug for the home button? I am aware having a finicky battery, and when its premature time comes, will have it serviced.