Killing apps on iOS can never hurt them (when they aren't the active app), unless the app is badly written. iOS will randomly kill apps when it needs resources (typically memory), so an app that can't handle being killed at any given moment will eventually have problems under normal use.
iPhones are rated
for 500 charge cycles (from 100% to 0% and back) before the battery will drop down to 80% of it's initial capacity. Unless she is doing something like heavy gaming 16 hours a day, there's no way she's anywhere near that limit.
If you want to test, do a backup of the phone via iTunes, then wipe it and have her use it for a day or 2. If the battery keeps draining then you have a hardware problem. iOS is so aggressive about killing and suspending apps it's virtually impossible to get that kind of drain unless you are actively using it constantly.
I'd chat with their online support before just grabbing a random 'Genius' at a busy store.