How do I loop a css animation with multiple keyframe definitions?

Without javascript I don't think you can. However you can achieve the same effect using a single keyframe animation.

.fade-bg {
  animation-name: fade-bg;
  animation-delay: 0;
  animation-iteration-count: infinite;
  animation-direction: forward;
}


@keyframes fade-bg {
    0% {
        opacity: 0;
        background-image: url('image-1.jpg');
    }

    25% {
        opacity: 1;
        background-image: url('image-1.jpg');
    }

    50% {
        opacity: 0;
        background-image: url('image-1.jpg');
    }

    51% {
        opacity: 0;
        background-image: url('image-2.jpg');
    }

    75% {
        opacity: 1;
        background-image: url('image-2.jpg');
    }

    100% {
        opacity: 0;
        background-image: url('image-2.jpg');
    }
}

EXAMPLE

I'm not sure this is possible with just css, but if you set up a setInterval method in JS cleverly, you could probably simulate the same thing by splitting the class into two.

var index = 1;

function switchBackground() {
   if (index == 1) {
      //this switches to  the first background
      var div = document.getElementById("yourDiv");
      div.className = "fade-bg-1";
      index = 0;
   }
   else {
      //this switches to  the second background
      var div = document.getElementById("yourDiv");
      div.className = "fade-bg-2";
      index = 1;
   }
}

setInterval(switchBackground(), 6000);

With .fade-bg-1 and .fade-bg-2 being the two animation classes.

Here's a jsfiddle if you want to play with it.