prevent :after element from wrapping to next line

JSFiddle - http://jsfiddle.net/Bk38F/65/

Add a negative margin to the pseudo element, to compensate its width:

ul li.completed a:after {
    background:transparent url(img1.png) no-repeat; 
    content: ' ';
    display: inline-block;
    width: 24px;
    height: 16px;
    margin-right: -24px;
}

Now, that is going to make the icon overflow the container, and the line is going to break only when the text meet the end of the line. If you need to maintain the icon inside the original container width, you can add padding to compensate again:

ul li.completed a {
    display: inline-block;
    padding-right: 24px;
}

---

IMPORTANT UPDATE:

For this method to work, there must be no white space between the text and the closing tag of the element holding the pseudo element. Even though the pseudo element's width is compensated by a negative margin, the white space will make the line break when it meets the edge of the parent element. For example, this works:

<span>text goes here</span>

and this doesn't:

<span>
    text goes here
</span>

you can add the image to the last word instead. that will make it break together.

add a class to word <strong class="test">word</strong>

and .test:after { ...

http://jsfiddle.net/52dkR/

the trick is also to make that class to be inline-block

and if you want to keep the underline see this.

http://jsfiddle.net/atcJJ/

add text-decoration:inherit;

This is a little similar to a previous answer, but I thought that I'd flesh it out and explain it fully.

As soon as you set display: inline-block, :after becomes a non-text-binding element. This is why it wraps, and why nowrap has no effect. So leave display alone.

As it's a text element by default, the content binds to previous text, as long as there's no whitespace between them. So don't add any, but make sure you have content: "", or it's the same as display: none. The only problem is height and width are controlled by the content, which in this case is collapsed. So width is 0, and height is the line height.

Resize the area with padding; left or right, it doesn't matter. Add a little margin so the icon doesn't touch the text. Keep everything as relative sizes (em, pt, etc.), and use background-size: contain, so that the icon scales with the text, like an emoji or font. Finally position the icon where you want with background-position.

ul li.completed a:after {
  content: "";
  background: url('icon.svg');
  background-size: contain;
  background-repeat: no-repeat;
  background-position: center center;
  margin-left: 0.2em; /* spacing*/
  padding-right: 0.75em; /* sizing */
}

I've used this for my external links (a[href*="://"]:after), and it's worked fine in Firefox, Chrome, and iOS. And since the icon remains a text element, even direct text after it binds, so any closing punctuation will wrap too.