There doesn't seem to be any solution to this problem, at least with my Z77X-UD5H, rev 1.1. I have tried three different Firewire 800 cards, the Startech, the Syba and an i.connect 800 card that I happened to have lying around. All three cause the same issue - no sleep(screen shuts down but fans, etc. keep running and it won't wake up), no shutdown(fans, etc. keep running after screen goes dark), though restart does seem to work. Tried just about everything I can think of, but no change. The only Firewire cards that do work and don't cause problems are some Firewire 400 cards that fit into the one PCI slot on this motherboard. Curiously enough, when I try the PCIe card(namely the Syba SD-PEX30009) in a Z77X-UP5TH, rev 1.0, the card and the computer appear to work perfectly - goes to sleep, wakes up properly, shuts down OK - not an exhaustive test by any means... but why the difference? These two Z77X boards are practically identical(same i7-3770K processor is being used in both), except for the Thunderbolt ports on the UP5TH. The bios on both boards is set up the same, and the bios on each is up to date(no beta versions, however). One has a 660ti video card, the other a 560ti, but switching the video cards back and forth did not change or fix the problem. Used the same SSD drive to boot both boards(OS X 10.8.4), so it couldn't be a software problem. This all points to the UEFI bios as being the source of the problem. But it doesn't sound like Gigabyte is about to tackle this one, even though it's pretty clear, at least to me, that something in the UEFI bios is to blame.
PS: I ordered and tried a PCI Firewire card, the Syba one that has both 400 and 800 ports, much like their PCIe card. The 400 port worked fine, so did sleep and shutdown, but the 800 ports did not. Anything connected to the 800 port wouldn't mount, and the computer would hang as well, forcing a hard restart...