I've found a solution to this issue. It generally happens when you paste text from another source, and it applies the html from the previous source confusing the WYSIWYG editor.
I'm currently using Evernote for Mac, so I can only speak about this one. But here's the easy fix:
Select all
Copy
Paste Plain Text by pressing Command + Shift + V
Now when you add line breaks, they will remain, since we've "reset" the html editor
Note: this will remove all your formatting and any images.