It seems like WMP has serious problems with syncing to large external drives, but no problem with smaller Flash drives.
In the thread Windows Media Player 12 and USB Drives, some people have reported success
after reformatting their external drives in NTFS, others rather with FAT32.
I have reproduced the problem with my own large external disk, but have no intention of reformatting it.
Even when successfully synced, WMP will sometimes insist for no reason on converting
the music to other formats when copying externally.
Some people have tried to solve this problem by keeping their music only on the external drive, since WMP will happily import music files from it.
This introduces more problems when the drive
is to be turned off, as treated in this article.
In conclusion: You could try to reformat the drive as NTFS or as FAT32 and it might work or not,
or some other weird problems might follow this first success. All in all, I think WMP sync
feature is too full of bugs to be called reliable. I really suggest using some other and less problematic sync product.