Shiu proposed 4 or 5 times to Toji because Toji keeps selling the ring for cash, and everytime Shiu realizes Toji "lost" it, he buys a new one and proposes again. At some point Shiu notices the pattern and understands that Toji is doing it on purpose, so he yells at him about being a disrespectful and ungrateful brat. But the day after he still buys another ring and brings his boyfriend to a really nice spot to propose once again. He also signs Toji for a really good job so he wouldn't have to sell the ring again. Toji also learns to deal better with his money and his bets now that he's in a serious relationship and he's happier than ever. Yet he still loses the ring, or pretends to. Shiu sighs and scolds him again, only to show up with another ring two weeks later. He knows his boyfriend is an idiot but he loves him anyway, so no matter how many time Toji throws it away for some cash, Shiu will still promise to stay by his side forever.
The thing is, Toji doesn't sell the rings anymore, he doesn't need the money that desperately. He hides them now, because he enjoys watching Shiu kneeling in front of him and confessing his love. It makes him so happy to listen to the man he loves asking him to be his husband, over and over again. And it's so reassuring that no matter how many times he betrays Shiu's trust and lies about the rings, Shiu will still love him. He loves feeling loved, as a man who grew up without any affection, this is like a drug to him. So he hides the rings in a box itself hidden somewhere, just to have his man listing everything he loves about him again. And the best part of this is that Shiu doesn't even mind, he's ready to propose as many times as needed, even if it's been years and they're still not married, it's alright, the love is enough.