I have a seagate external 1 tb external hard disk. It's USB doesnt work properly, whenever i plug in it takes time and lots of efforts to detect. Once it connects it doesnt copy the files and now-a-days it keeps telling me to format it without letting me access my files. I have 250 gb files in it. Cant format.
If it is just the USB part: Take the disc out of its enclosure. Put it in a desktop, an external dock or another enclosure and make the backup.
I have a sea gate 1.5 go flex USB2 storage devices. It had a similar issue and I did the following and it has not had a problem since.
Not knowing how old the unit is, I would suggest trying non case opening methods first. If you open the case, you void your manufacturers warranty (if it is still applicable) and you may need that if you have a failing drive and need to RMA.
I used MiniTool Partition wizard home edition (free) to run a Check File System (it's faster than windows). I ticked Check and repair. There where file errors and it fixed them.
Once done I choose align partition. In my case, partition needed to be aligned. If your doesn't need aligning, it will tell you.