Honestly, the problem may be the size of the drive. The fact that these TVs work with external hard drives is purely coincidental with that the fact that they were designed to work USB flash drives of 16, 32, or 64 GB. Sure, the terabyte drives work, but the TV takes an eternity to index them and then recheck their contents when accessing them again. So Bob's advice he often times gives is to go with a smaller drive: it'll connect up much more quickly that way.
I have been using my 6 series TV (es37ue6300) with a 1 TB WD drive and Allshare Play.
Firstly it worked ok, taking a couple of tries to get into the file menu (AllShare / Video / USB device).
Then it started taking 5-10 tries.
Now I cant get it at all.
It still reads the memory (644GB of 1TB in use). It also still lets me play videos from "My List". So it is obviously still connected.
However when I try to go in through AllShare / Videos / USB it thinks for 2 minutes then says "USB Device Disconnected" then thinks, then comes up with "USB Device connected, Videos / Music / Photos" and I repeat the whole process!
I have the latest firmware and the HDD works with my PS2 fine.
I dont have a computer at the moment so it is particularly frustraing as I don't have any way to stream to my living room TV.