The ‎<blockquote> element and any templates that use it do not honor newlines:

Markup Renders as
<blockquote>
Line 1
Line 2
Line 3
Line 4
</blockquote>

Line 1 Line 2 Line 3 Line 4

The simplest workaround for this is to use the <poem> tag inside ‎<blockquote>, which will convert line breaks to ‎<br /> tags:

Markup Renders as
<blockquote><poem>
Line 1
Line 2
Line 3
Line 4
</poem></blockquote>

Line 1
Line 2
Line 3
Line 4

To markup actual paragraphs within block quotations, entire blank lines can be used between them, which will convert to ‎<p>...‎</p> tags:

Markup Renders as
<blockquote>
Paragraph 1

Paragraph 2

Paragraph 3
</blockquote>

Paragraph 1

Paragraph 2

Paragraph 3