The solution is here:
http://rt.cpan.org/Public/Bug/Display.html?id=40261

Quote:
I think the module can be fixed very simply by commenting out two lines.

# $protocol->parse_head($parse_head);
# $protocol->max_size($max_size);
[download]

These are lines 1496 and 1497 of LWP/Parallel/UserAgent.pm.