Disconnecting Bluetooth seems to have solved this problem for me. Strange, hey?
I have a MBPro Early 2011 model to which I added a TBD about 2 years ago. Like the original poster of this thread, I use all the rear ports of the TBD to charge and connect iphones, ipads, external hard drives and (occasionally) a mouse. This leaves my working space cleaner and allows me to use the few ports available on the MBP for incidental use. My printer is connected wirelessly through a time capsule.
When upgrading to Yosemite in late 2014 all functionality of my TBD usb ports vanished. As I made the upgrade at the same time as upgrading my phone to iOS 8, I couldn't originally tell whether this was a phone, computer, or TBD issue.
I've done all the usual things which people recommend... restart; reinstall; PRAM; SMC etc. Have called Apple. Have visited the Genius Bar.
By way of comparison, my MBAir is still running Mavericks. The TBD usb ports are fully functional when connected to my Mavericks device.
One commenter in this thread (I can't find it now!) suggested they had fixed the functionality issues by disconnecting Bluetooth from their devices. I've just done the same, followed by a restart. All my functionality of the usb ports through the TBD has been restored - that is, while running Yosemite through the MBPro. All external hard drives are operational again; phone is charging; image capture is working; itunes is connected to iphone.... This is the first time that the system has worked since Yosemite was installed 6 months ago.
I don't daisy-chain to other displays, so can't give any feedback on whether it would work in such a case. Nor do I use a wireless keyboard, sorry.
I'll report back if the situation changes.