For such an old and recurring problem I was amazed how little help I could find searching for an answer online. (Also searched here.)
My blockquote styles break when I hit the Return key. That is, only the first paragraph contained in a blockquote shows the styling.
Here you can see that i've instead wrapped each 'graf in its own blockquote tags. a sorry excuse for a fix. But otherwise, as I said, only the first one shows style.
(ps, this is a mod of the WP theme "blogger upstart minim")