IPhone 4s has battery, won't turn on?

A few days ago, I wanted to use my iPhone and it wouldn't turn on-it was completely blacked out. I tried holding down both buttons, but it just wouldn't turn on even though it had battery and I had used it a few minutes before. I then plugged it in and it turned back on. Today, it happened again where it blacked out, and wouldn't turn on even when I held down both buttons. I plugged it back in and it turned on. Then it happened for a third time, and I had to come back home to plug it in to get it started again.

Any ideas why this is happening and how to stop it?

I would call the Apple customer service, they will resolve very quickly!