perl -p walks over each individual line of each input file, so the match /\n\n/ will obviously never be true (a single line can't contain two newlines)
If the files are not too large, you can ofcourse slurp them entirely into memory and then do the substitution:
perl -0777 -pi.bb -e 's/\n\n/\n/g' filename
(that's a zero, not an o)
otherwise you'll need a bit smarter script, like: perl -pi.bb -e '$p&&s/^\n//;$p=/^\n/'
BTW, if you just want to filter out blank lines, you can do:
perl -pi.bb -e 's/^\n//' (which is like doing perl -0777 -pi.bb -e 's/\n+/\n/g' except more efficient) | 