Seagate external HD light blinking, not detected on mac, help!

Hello all, I have purchased separately two Seagate external hard drives (one for mac,slim) (other just plain doesn't state for mac or not, (not slim) with in a year and half of each other, the cord for both kept ejecting on its own. its very sensitive, almost to sensitive, i cannot so much as type and it comes out disconnecting the disk from my computer. Therefore, my time machine doesn't fully backup, I don't know if it has ever fully backed up at all. Now on the newer Seagate I went to recover something from it and the light is blinking but its not being detected on my mac. I tried to plug it from my Mac Air to my Mac Pro, same thing.

Then I tried the older Seagate, just my luck that too is blinking light, not being detected on my macs. Help!? is there a program I should download to fix this, are they corrupted disks now because they were so often disconnected improperly? every 3-5 minutes. Should I get a different cord for both, does anyone think if I try the disk not for mac on a windows, that it might work? Is anyone else having this annoying problem?