After what happened to Naofumi early in the story, he sank into a depression. This expressed itself through various symptoms, such as apathy and being unable to smile. He actually sunk deeper in the Light Novel, where he bought Raphtalia to pretend Myne was his slave. Feel free to click the links above to read the relevant articles about this on the site.
Naofumi could not taste and could not see Raphtalia grow up because he was depressed. Although it is a little exaggerated in the anime, there is at least some basic scientific basis for depression affecting the senses.
While most of the other symptoms of Naofumi’s depression made sense, these two admittedly seem pretty far-fetched. It’s not actually nonsensical though, as explained below.
Naofumi’s Depression Messes up His Senses
Research has shown over and over again that depression has a noticeable effect on your senses. Being depressed is both the result of the input into your senses, as well an influence on your senses. Senses are both a part of the problem and the solution, which explains the difficulty of overcoming depression.
Sight
When you are depressed, you have difficulties perceiving contrast, making the world appear more grey. This is very visible in Episode 4 after Naofumi “loses” the duel against Motoyasu.
Stress and anxiety also make you see things that are not there (or, in Naofumi’s case, not see things that are there). We may also be extra sensitive to light when depressed. However, we also need light to activate our brains and fight feelings of depression.
Taste
Certain chemicals are less present in the brains of those with depression, reducing taste. Of course, it’s not quite as bad as not tasting anything at all, but there is at least a base of realism in Naofumi’s lack of taste. Recovering a sense of taste helps with depression, so here too it’s a bit of a vicious circle.
Smell
The sense of smell is closely intertwined with taste. The part of the brain that is responsible for smell is smaller in those with depression.
Hearing
Those with depression often suffer from noise sensitivity. This leaves them more irritable, as we can see with Naofumi, mainly in the early story.
Touch
Depression causes you to be more sensitive to touch and pain. That last element luckily seems to be offset by the fact that Naofumi is the Shield Hero.
Sensory Overload
As you can read above, you are more sensitive to a lot of sensory impulses when depressed. This can cause you to have more sensory input than your brain is able to handle. Those suffering from sensory overload feel overwhelmed, which is not exactly helpful for combatting depression.
We actually see a pretty clear example of this in Episode 4 of the Anime, after the duel against Motoyasu.
Conclusion: Is Naofumi’s Depression Realistic or Not?
At the very least, there is a base of realism in the way it is shown.
The Rise of the Shield Hero is still an anime, however, so things are naturally shown in a more over the top way. Both the symptoms as well as the sudden snap back to a more healthy mood are not realistic in the strict sense of the word. The author however clearly researched the topic and uses enough realism to keep our suspense of disbelief.