Maybe because of his current wife. When you think about it, the current Grand Duchess really wants a daughter and she was given a chance to have one as soon as Nera appeared with her sudden "red eyes". It's obvious why the Grand Duke didn't do anything about it like investigating or making sure Nera was his biological daughter. He must have had some type of fall-out with Iris's mother, Rose, and he feels guilty to suddenly take interest on what Rose has been doing or the events in her life before she died. You wouldn't take any interest to what happens to your ex if the breakup was really bad or severe, right? Who knows what sperated them? What's the secret between the Grand Duke and the Grand Duchess (referencing to the episode when she said "He's a kind man who even married a woman like me."
We also have to take notes on why Rose kept the pregnancy from the Grand Duke. This fact might be related to the three of them (Grand Duke, current Grand Duchess and Iris's mom, Rose) in a complicated way, for example, either Rose couldn't marry the Duke or vice versa, and so the Duke had a political marriage with the current Grand Duchess.
Even with all of the clues and foreshadowing, the situation keeps getting complicated, and now that Sophie is brainwashed to believe that she's a Count's daughter, it might take a very long time for Iris to find out she's the blood-daughter of the Grand Duke. It might happen after Iris saves Sophie from the brainwashing.
The Grand Duke is standing 3 feet from Iris. How can he not notice that she has red eyes too? Also, did he do the smallest investigation into Nera? Did he not manage to find out that his ex had a daughter called Iris and not Nera? And that She also has red eyes? How exactly did he get confused?