USB drive keeps disconnecting and reconnecting

Solution 1:

It's over two years later but I figured I may as well answer this question just in case anyone else ever has the same issue.

It turns out that one of the USB2 ports on this old MacBook Pro was not working properly. Not sure exactly what the issue was, but I ended up buying a USB3 expansion card to get better speed out of the drives, and after using that both drives performed perfectly. This is the first and only time I've ever had a USB port actually be the cause of a problem like this.

Solution 2:

Maybe the replacement drive isn't exactly identical and requires a bit more power. Disconnecting and reconnecting is typical for underpowered drives. Try to connect external power source if the disk's enclosure supports it.