I also used s%%% instead of s/// to avoid the need to backslash the slashes in endtags.

s%(<p>(?=(?:(?!</p>).)*\n\n)(?:(?!</p>).)*</p>)%-->$1<--%sg
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Explanation:

The p-tag must be followed by two newlines that aren't preceded by its endtag.

You can make the regex more readable via /x :

    s{ (<p>
         (?=(?:(?!</p>).)*\n\n) # Followed by two newlines not precede
+d by </p>
         (?:(?!</p>).)*</p>)    # Followed by </p> not preceded by </p
+>
     }{-->$1<--}sgx;
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Update: or even

my $not_followed_by_end_p = qr{(?:(?!</p>).)*}s;
while (<>) {
    s{ (<p>
         (?=$not_followed_by_end_p\n\n)
         $not_followed_by_end_p</p>)
     }{-->$1<--}gx;
    print;
}
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($q=q:Sq=~/;[c](.)(.)/;chr(-||-|5+lengthSq)`"S|oS2"`map{chr |+ord
}map{substrSq`S_+|`|}3E|-|`7**2-3:)=~y+S|`+$1,++print+eval$q,q,a,
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