Look at RFC 1945 page 11; this is a violation of the HTTP spec.
I suspect the BigIP rejects it.
$fullbody =~ s/\n/\r\n/mg;
at around line 610 of jlj.pl fixes this.
(And this is why it's better to use a Perl HTTP library: less code means fewer bugs. The next version of LoserJabber uses an HTTP library for this very reason.)
I suspect the OS X client has a similar problem.
Also, to the Mac users: your HTML problems with LiveJournal will be addressed eventually. Appreciate that both Brad and I have finals next week, and we really shouldn't be doing things like tracking down bugs in other people's LiveJournal clients. :)