Why are Finder shortcuts to Ext HDD removed whenever it's not connected? Workarounds?
You don't say how you created the "shortcuts". If you used Finder to make Alias OS X creates a complex (and very large) file. These are probably OK, if you want that kind of thing, but OS X has functionality to locate files if they move, and presumably doesn't show them if not present. (I can't verify this as I don't use Alias, except for software testing, and never to external drives.)

I suggest you create symlinks, which are much smaller,and hang around, even if the target disappears. Unfortunately the only way to create symlinks is with a command, although I have created a Service to run this in Finder.

The following is an script, which I run as an Automator workflow.

for f in "$@"
do
 fileSuffix="link"
 fileExists=`ls -d "$f $fileSuffix"`
 fileNumber=0

 until [ $fileExists=="" ]; do
  let fileNumber+=1
  fileSuffix="link $fileNumber"
  fileExists=`ls -d "$f $fileSuffix"`
 done

 echo "$f $fileSuffix"
 ln -s "$f" "$f $fileSuffix"
done