It looks like I've cracked the case on where Global Crossing just is plain wrong, with the help of Bernard, who pointed me in the right direction.
I did some tcpdumps on the IPv6 session for Neighbor Discovery and Solicitation, which uses ICMPv6 and is crucial in the interaction of IPv6 hosts. And guess what ? They are even rate-limiting that !!! No wonder, we're constantly loosing the connection to their router.
Anyhow, I've dumped more data including the tcpdump to them and we'll see, what they say to that.