Q: Phone stuck in recovery mode

My iPhone 5c has just recently started shutting off when it's not even close to dying. I would have to force restart it. Today, it turned off again, but this time it won't turn back on. It's been on the charger for hours. I've discovered that it is in recovery mode and when I plug it into iTunes it gives me the option to restore my phone. I clicked the button and it restored for a half hour, but then at the end said that the phone can not be restored. I've read that sometimes you have to toggle the mute button and then it will turn on, but that didn't work for me. What is going on?