It is entirely possible that the battery is a dud. While iFixit sells some of the best quality batteries out there, there's bound to be a bad one here or there. Did the replacement battery ever work properly or did it just start happening all of a sudden after a week? Is it doing the exact same thing as the original battery? You can always try to install the old battery, if possible, to see if the problem is consistent regardless of the battery or unique to an individual battery.
If the problem is identical, the there is probably another component in your phone that is drawing too much current. It could be the screen or camera of sensor flex.
Contact iFixit Support to see what options are available.