Doesn't sound like a problem of "what's killing my battery?" It sounds like it stops charging, which is probably a hardware issue...either the battery, the charger, or the phone.
Try a different charger. If it still does it, try a different battery. If it still does it, return the phone.
FYI, the way charging works is that once the battery hits 100%, charging stops to prevent the battery from overcharging and starting a fire. It will drain according to background tasks and communication with the tower and/or wifi. Once the battery hits a certain point...usually around 95%...it starts charging again until it hits 100% and then shuts off again. If the charger kept charging after the battery hit 100%, the battery would heat up, melt, and start a fire.
Seems that your phone is not picking back up at the 95% mark. Are you running a custom ROM? If not, I think this is a problem with either the charger or the phone.