Device Turns off Randomly when, charged returns previous battery life?

I dropped my Moto x force and the battery was damaged as well as the front facing camera. I haven't replaced the camera but have replaced the battery. The phone charges and will work perfectly for a few hours, without overheating. Then after a few hours (normally about 2 hours) just turns off and then doesn't turn back on until its charged for a little bit. Were it will return to its previous battery life.

If their are any other questions you have about it I will be happy to answer.

Thanks