Not all mixers use this “unique code” to avoid receiving their old coins. But for those who do, that’s the explanation I got from BestMixer from when I asked them about this specific functionality they use.
And how does the code thing works? How can you link someone's mixed coins to a code (to avoid receiving the same coins and to give special discounts to 'loyal users') and ensure anonymity at the same time?
It's very simple. We mark each address in our pool (only the address, but not binding to the visitor of the website) with a unique key, that does not allow anybody to get the same coins back when re-use BestMixer service.
Of course there is no way of knowing if all the other mixers function this way, but due to their anonymous nature, I assume they do something similar (unless they are a honey pot).