I can't see how that could even "kind of works". According to the perlrun description of the -p switch your code provided on the command line is wrapped in:

    while (<>) {
        ...             # your program goes here
    } continue {
        print or die "-p destination: $!\n";
    }
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which deals a line at a time so your regex will never match. For such a multi-line matching regex to make sense you need to slurp the whole file into a string and run the regex on that. The easiest way to do that is write a small script rather than try to shoehorn it into a "one liner". However that gets to be a whole lot more work because you then have to handle things a file at a time instead of using Perl's -i and @ARGV magic in a simple fashion. However, with just a little work we can still use the magic:

use strict;
use warnings;

my @files = @ARGV;

$^I = '.bak';

for my $file (@files) {
    local $/;
    @ARGV = $file;

    while (<>) {
        s/\n\n/\n/gs;
        print;
    }
}
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