Hi,
If you're not using Falang, then HikaShop relies on the translations override file system of Joomla to store the translations. For that, it takes the original text and use it as a key and the translated text as a value.
So if you have the text "hello" as the name of the product and you enter the translation "world" for it, in the translations override file, HikaShop will add the line:
HELLO="world"
And if there is already a translation key "HELLO" in the override file, it will replace it.
So for example, if you have the same text for the product name of two products, if you change the translation of the name of one, it will change it for the other one.
Now, I don't see why the translations would become empty on the original product when entering translations on the copied product. That doesn't make sense based on how the system works.
Could you create a test unpublished product and fill in fake text and translations for it, and copy it and translate the texts of the copy ? Are you able to reproduce the problem ?