Fade out after div content has been shown using CSS

Using css3 keyframe animation:

(You'll probably want to add -webkit- -moz-, -ms-, and -o- prefixes on the animation and animation-delay properties inside .error-message and on the keyframes to support older browsers.)

.error-message {
    animation: fadeOut 2s forwards;
    animation-delay: 5s;
    background: red;
    color: white;
    padding: 10px;
    text-align: center;
}

@keyframes fadeOut {
    from {opacity: 1;}
    to {opacity: 0;}
}

<div class="error-message">
    <p>Some random text</p>
</div>

You can use animation example.

Set the animation-delay to the time you want. Make sure you use animation-fill-mode: forwards to stop the animation.

#signup-response{
    width: 50%;
    margin-left: auto;
    margin-right: auto;
    text-align: center;
    background-color: #FF0000;
    margin-top: 20px;

     animation:signup-response 0.5s 1;
    -webkit-animation:signup-response 0.5s 1;
    animation-fill-mode: forwards;

    animation-delay:2s;
    -webkit-animation-delay:1s; /* Safari and Chrome */
    -webkit-animation-fill-mode: forwards;

} 

@keyframes signup-response{
    from {opacity :1;}
    to {opacity :0;}
}

@-webkit-keyframes signup-response{
    from {opacity :1;}
    to {opacity :0;}
}