1. Same problem with 3 FW800 LaCie drives, 2 different Macs just updated to Mavericks (a nasty, nasty place, as surfing spots go). Drives never power down, even with computer power off. One is a brand new MacBook Pro with mechanical drives and no Retina display. The other is a 2009 iMac quad core i7.
2. The iMac goes to white screen of death when I try to do a shutdown. Ultimately the screen goes dark, but there's still internal drive activity, etc. The only escape is a forced power down (long press of power button). Its LaCie is a 2 TB RAID in two 1 TB partitions. One partition is a (hopefully still) bootable "Restore" disk of Show Leopard. The other is dedicated to Time Machine. Did a Disk Utility check of the partitions, and both seemed fine.
3. This morning (that's after not sleeping 'til 4AM, so 'morning' is relative) I 'erased' the Time Machine on the iMac's FW800, and just finished creating a new Time Machine backup. Note: When Mavericks was installed, the icon for that partition turned to the orange FW generic, but kept the Time Machine name. As soon as the new Time Machine was created, the green Time Machine icon was restored (Yay!).