Battery shut down

I was in USA last August an I went to Apple Store in LA to fix the issue. The technical support representative made battery test that showed the battery was in good condition. Then he said that I had to do a complete erase and restore again to see how things go, which then I had to do at home.

Complete erase and complete restore was done and yet the problem was not solved.

I then went to another Apple Store where the technical support representative told me that I might have software issue, and he recommended me to erase and restore as new phone with erasing all applications and getting my old contacts only. I did that and again the problem is still annoying me.

What would be the best solution to it?