Answer by Nisse Engström for Updating an old answer broke all of the links

Here's what the Markdown help has to say:

Block-level HTML elements have a few restrictions:

1. They must be separated from surrounding text by blank lines.
2. The begin and end tags of the outermost block element must not be indented.
3. Markdown can't be used within HTML blocks.

<pre>    You can <em>not</em> use Markdown in here.</pre>

Point 3 is what's most important here. It's much easier to use Markdown all the way than trying to mix it with HTML. You have a lot of […][…] style links inside <p> and <blockquote> elements. You need to change the links to proper <a> elements, or (perhaps preferably), replace your HTML with their Markdown equivalents:

• Blank lines between paragraphs.
• > prefix instead of <blockquote>···</blockquote>
• **···** or __···__ instead of <strong>···</strong>

If you need more than one block level element inside a list item, you need to prefix the subsequent blocks with four spaces to continue the list item. Without this prefix, the next block will start a new list item.

It is possible that the rendering rules have changed since you last updated your post. The rendered HTML is stored together with the Markdown and is not re-rendered until the post is edited.