Did you format the drive first? You have to format it from Disk Utility first before macOS recognizes it.
If that isn't the problem, it may be your hard drive placement. What type of hard drives are you using, solid state or hard disk? Which one is in the caddy? Which one is the boot disk?
I had a problem like this with a 500GB SSD as the boot drive and a 2TB HDD in the caddy. The 2TB would stop being seen after a few minutes of inactivity (I think because of the power draw and the way Mac handles power to the ODD). I switched the disks, putting the 500GB SDD boot drive in the caddy, and no ones complained since.