Destroying the original object destroys all its clones?

As the question's title would imply, I'm trying to destroy a GameObject without destroying instantiated clones of said GameObject. However, this doesn't seem to work. The clones can be destroyed, no problem, and they don't interfere with one another. However, if the original is destroyed, they all get destroyed. Here's an example of something I tried:

 if(Time.time - timeToDestroy > 0 && canDestroy)
 {
      Destroy(gameObject);
 }

The clones are not children of this object, and I have checked them, at run-time, and they are, indeed marked with the boolean field canDestroy as false, whereas the original has it marked true (I set up a simple timing system to manage this, as is noted in the code above).

I would greatly appreciate it if someone could explain to me why this is happening, and how I could avoid it without needing to add all the components and set all the values manually, creating each individual "cloned" object by hand... Thanks!