Can a Digitizer use a design for more than one client?

yes this is absolutely correct!!!

At our factory we retain the design of the customer although they have paid for it. We will not charge them again when they reorder but we are just protecting and securing our business. We pride ourselves in our digitizing and none of our competitors can make designs like us so by giving away our designs, we will be loosing out on the actual orders because the competition does the actual embroidery much cheaper than us. We get our price for embroidery for the good quality digitizing as well as the quality of embroidery.
This is just the way business has to be done I guess!!

I disagree with this. I've been told it only applies if the design in question is trademarked or copywrited. And in the event you use the design in question, and change it somewhat but it still reflects a similiar appearance, then it's up to a court to decide if it's infringement or not.

Furthermore as I'm told, the physical design itself, as to the .dst or whatever file format as it's in your computer memory, does not belong to the customer, only the design as it's used in whatever fashion, belongs to the customer, on a garment or hard item. As I understand that,,,,,the customer that paid you for the file can request you give, or sell, it to them, but you're not bound or obligated to do so. You can do as you wish with it, as I said above, give it to them, sell it to them, or delete it. They can instruct you not to use it. And, they would have to prove that you did use it should they see it elsewhere. Again, I'm told this applies only if it's trademarked or copywritten.

I'm not a lawyer obviously. It's a shame the business has taken a turn in this direction over the years,,,,