My Seagate Backup Plus 4TB USB Drive will no longer stay mounted
I have a 2013 iMac 27" with 750GB SSD and i7 running latest release of Mavericks OSX 10.9.3 (13D65) and have been using a Seagate Backup Plus 4TB USB Drive exclusively for Time Machine Backups. Seagate's Website says the Drive has the latest Firmware Update (I checked because earlier posts suggested this as a solution to similar problems). The Drive and Time Machine worked great together until 20 days ago when Time Machine Began reporting that the system had not been backed up recently (I should say it now reports it has not backed up in 20 days.
I can temporarily remount the drive by unplugging it from the USB Port and it's external Power Supply and rebooting the iMac and then Powering up the Drive and then plugging in the USB Cable. This is how I was able to check on Seagate's website to make sure the firmware was up to date. It will begin a Time Machine Backup and then give an error message stating Do Not Remove the Drive without Ejecting It Properly. I have not tried to eject the drive it simply stops being recognized by my iMac.
Time Machine sees the various Backups while the drive is working and will try to start a backup but then simply stops seeing the drive after 2-5 Minutes. The USB Drive was formatted by OS X Mavericks and as I said worked fine for several months. I do extensive Book Design and App Development for a Ministry I volunteer my time for and for my local church and I am very concerned about not having a current back-up. My USB Drive reports that it has a little over 3TB of available space of 3.64 TB total so this is not a question of lack of capacity.
I welcome any thoughts and suggestions. I am relatively new to the Mac World (this is my first Mac in many years) and although I know how to diagnose and usually correct issues with a Windows PC I am not there yet with the Apple Mac environment. I am a long time user of micro computers and am generally viewed as knowledgeable and capable. In fact I used to own a chain of computer stores that sold Apple, IBM, Compaq, HP and other brands but that was many years ago so I am only recently a Mac User again.
Thanks very much for anyone viewing this and offering suggestions - I really appreciate any help.
iMac, OS X Mavericks (10.9.3), iMac 27 750GB SSD i7 3.4 GHz 24GB