A "line break" is simply a blank line between sentences or paragraphs (much like the space between this sentence and the one above it).
I had this problem for about a week and it drove me crazy, I was sure it was a Wordpress problem until I discovered it was actually an issue with my theme.
Here are the symptoms ... These tags will not cause line breaks (returns) as they should :
<br />
<br>
<p>
</p>
Look inside your Wordpress theme css file and see if you can find something like this :
p {
margin:0px;
padding:0px;
}
If you do try removing it (only after making a backup of the code) and see if that works.
I had two instance of that type of code which was controlling how my post looked. After I removed the above type of code everything worked like a charm.