I haven't used ping in a while, and I can't say whether this is the source of your problem, but I remember reading that trying to send a ping from your program/user (as with Net::Ping) is not always reliable because it might actually require root privileges. Net::Ping::External is a workaround that calls an external ping program.

use Net::Ping::External qw(ping);
my $alive = ping(host => "www.perlmonks.org");
print "alive: $alive\n";
[download]

Might be more reliable on those OSes supported by Net::Ping::External.