Is it possible to have cordial status with pirates at endless difficulty?

Yes, it is possible to have cordial status with the pirates on endless difficulty. I don't believe your issue is related to the game difficulty. I have encountered the same issue where your status with the pirates becomes "wary" even though you are sufficiently positive with them to be "cordial" and may even be so for a turn before it returns to "wary". I suspect the issue lies in some sort of code that is triggering that makes the pirates go into "wary" and I'm not entirely sure what that is. 

(Edit) It appears that Cat answered your question HERE. I suspect there may be some other possibilities that trigger the Wary status as well, but it seems its associated with another faction having a more positive (green) relationship. So, you would have to Support them with more money until you are higher.

Cat-o-nine said that wary is almost the same as cordial, Wary happens, when another empire is paying more dust to the pirates, so THEY have become cordial. And not you.

It is filed as a bug, because the tooltip could be clearer.

(Oops DustWhit. You beat me to it :) )