iPhone 6S Plus Faulty Battery?

[invisibleshoes]

Hi, I have a new 6S Plus just purchased a few days ago. I'm waiting to give it to my mother so I've charged it up full and turned it off. Problem is, every time I turn it on again, the battery is completely dead with the battery screen present. Happened twice. Is this a faulty battery? Seems like the case of the screen always "on" even though it is off.

 

[CNeufeld]

Something sounds defective. I'd take it back pretty darn quickly.

C