A quick refresh, I have 6 drives plus 3 usb sticks all were failing to register on my 2010 iMac 27" running mavericks. All was fine before upgrading then slowly and intermittently they started to fail to register, finally when I updated to Mavericks OSX 10.9.1 nothing but SD card and randomly one USB Stick could be found when plugged in...
It is important to add that I had a variaty of extenal drives WD, Seagate, integral, Toshiba and formated in different ways NTFS, FAT32 & Mac OS Extended (Journaled)
I found a solution there is more good news than bad for sure, however it does come in 2 parts..... Good news the actions on this page helped disk utility locate my external drives connected to my Mac, HOWEVER they would not mount http://support.apple.com/kb/HT1379?viewlocale=en_US&locale=en_US then for good measure follow that up with the the instructions here http://support.apple.com/kb/HT3964 part 2 was adding a little bit of software the bad news is that costs $20 (£15) called paragons this is available from http://www.paragon-software.com/partners/index.html not to be confused with the limited version for free you receive when you purchase a Seagate drive you need the full version and luckily they offer you a 10 day trial so if you have less sucsees than me no need to purchase it I am happy and all is right with my world on my lovely iMac and to be honest it was not that hard and takes easily less than 30 minutes with no complicated instructionsto follow...