CSS Animation property stays after animating

I think you're looking for animation-fill-mode CSS3 property

https://developer.mozilla.org/en/CSS/animation-fill-mode

The animation-fill-mode CSS property specifies how a CSS animation should apply styles to its target before and after it is executing.

for your purpose just try to set

h2 {
  animation: fadeIn 1s ease-in-out 3s;
  animation-fill-mode: forwards;  
}

Setting forwards value «the target will retain the computed values set by the last keyframe encountered during execution»

In addition to the answer of @Fabrizio Calderan, it has to be said that you can even apply the animation-fill-mode property forwards directly to animation. So the following should also work:

@keyframes fadeIn {
  0% {
    opacity: 0;
  }
  100% {
    opacity: 0.9;
  }
}

h2 {
  opacity: 0;
  animation: fadeIn 1s ease-in-out 3s forwards;
}

<script src="//cdnjs.cloudflare.com/ajax/libs/prefixfree/1.0.7/prefixfree.min.js"></script>
<h2>Test</h2>

I had something similar happening to me. I added position:relative to the element that was animating and that fixed it for me.

How to animate an element and get it to stay as the animation is done:

// Beggin

#box {
  /* Give it a width, a height and a background so can see it  */
  width: 200px;
  height: 200px;
  /* Unimportant styling */
  box-shadow: 0 0 10px 0 rgba(0, 0, 0, .4) inset;
  border-radius: 7px;
  background: linear-gradient(to bottom, #fff 30%, #fcfcfc 40%, #f8f8f8 50%, #f0f0f0 100%);
  
  /* Starts here: */
  opacity: 0;
  animation: yourName 2800ms ease-in-out 0s forwards;
}

@keyframes yourName {
  0% /* (from) */ {
    opacity: 0;
  }
  100% /* (to) */ {
    opacity: 1;
  }
}

<div id="box"></div>