Q: My seagate external hard drive is no longer readable but it used to be. Why won't my mac read it anymore?

see this article

https://support.apple.com/en-us/HT201639

it's possible if the drive can not be repaired the drive is damaged and should be replaced.

How old is the drive and is it still under warranty?

How is the drive formatted?

Control (right) - click on the drive's icon on the Desktop and select Get Info from the contextual menu.  The info window will indicate how it's formatted:

Your Seagate drive is probably formatted NTFS. Go to the Seagate website and download a dmg file called NTFS_for_Mac (or something like that). Seagate will have instructions. I just mounted the dmg, ran the prog and my drive now shows up.

Do you have the Finder preferences set to display external HDs on the Desktop?

Thank you -  this really helped me but I don't have the tick box which says ignore ownership at the bottom.  Still at least I can read the hard drive now. 

any management from the vendor for that drive may become problematic later. It's a good practice that if you use the drive exclusively for your Mac OS to not use NTFS as it does not support the Mac File System and relies on 3rd party tools or terminal hacks that have been cited as disastrous and the management tools from vendors often become incompatible with later iterations of the OS.