A couple of points that haven't been mentioned yet:
Perl's input record separator $/ has a special "paragraph mode" when you set local $/=""; that will split the input on one or more blank lines.
GrandFather mentioned the spaces in the regex. If you wanted to format your regex nicely and have whitespace ignored, you could use the /x modifier (perlre).
Cristoforo's suggestion is nice and short, but has the disadvantage that it reads the entire file into memory before grepping it.