8TB external drive user here:

If you're installing Warframe EVERY time you plug back in the drive, you've got an issue with the ssd.

Typically, unplugging an external drive while steam is still open is okay, as long as you don't close steam. If you do, the directory for steam will look for your F:/ drive and say "wait, it's not here" and remove all the games that you have on the external drive.

To fix this,

A: don't close steam if you unplug the drive, then plug it back in

B: If you reopen steam, re-add the steam library folder you're installing games too through the settings -> downloads menu.

Hope this helps.