Akiyama rarely reproaches Kiryu and, if he does so, it is for the understandable hurt of being lied to, mistrusted, excluded, not listened to. Or for the mistakes he thinks Kiryu is making.
However, Akiyama NEVER throws back in Kiryu's face the generous things he did for him, never brings them up to guilt-trip him, never holds any of that against him. Despite the fact that Kiryu stopped showing him any gratitude after a certain point, acting insensitively and neglectfully to him. Despite the asymmetry of effort and feelings.
There are many reasons he has for taking Kiryu's unfair treatment with almost zero complaints, and I will explain them soon. But, regarding this specific aspect of his behavior (never bringing up all the sacrifices he did for him and his incredibly generous offers), besides his perceived debt of gratitude towards him, the explanation is simple:
He didn't do all that because he wanted to be thanked, because he wanted leverage on Kiryu, because he wanted to make him feel guilty or indebted. He did it because he wanted to, because he loves him and really wants to help him, because he cares. So he takes responsibility for his choices and doesn't regret them, even in the face of ungratefulness and poor treatment. His conscience is clean, he knows he was being genuine, so he doesn't want Kiryu to feel that burden, he owns that as his own decision.
He developed that strength in the past, in the face of repeated betrayal. We see that side of him also with other characters, for instance in a bitterly self-aware talk with Yasuko that ends in a great act of generosity, even if he doesn't know her real motives yet. This behavior is also a way to have more control over his betrayal injury, to embrace some of that pain consciously, not to be surprised and destroyed by it. Just like his tests are also a coping mechanism regarding people's unpredictability.
His altruism, however, is not perfect. Not even towards Kiryu. He is human and struggles with selfish motives as well, although he eventually manages to minimize them in favor of more selfless intents. Even after Kiryu stopped having any perceived usefulness for his vision of Kamurocho: his love for him has become purely personal, and lasted long after Kiryu stopped being a yakuza, the Dragon of Dojima Akiyama hoped would rule the town.
Regarding the initial topic, a part of him also wants to feel needed by Kiryu, and would like Kiryu to want him in his life. Even though Kiryu clearly doesn't care about Akiyama in the least, doesn't love him personally, barely remembers that he exists, used and disrespected him so many times. That's why he is sometimes too pushy (we see it in Infinite Wealth) in self-inserting in Kiryu's life, even in the face of his blatant disregard.
Part of it is because Akiyama has a partial blind spot when it comes to fully acknowledging when someone doesn't love him back, or not as genuinely as he loves them (we saw it in his stubborn intent to keep pursuing Eri even after she acted like a golddigger and married Yamori, but we also see it in his Infinite Wealth outburst, where his words imply he expected Kiryu to act like a real friend to him and see him as one, when Kiryu never really cared about him in the first place).
But another reason are some hidden emotional needs and behavioral patterns of his I will highlight elsewhere. In any case, he never lets his selfishness prevail, his genuine kindness always wins in the end. With poor outcomes, that he can handle and usually decides to accept for a variety of complex psychological motives.