Ageing out of usefulness isn’t the only way that Tyson could find himself becoming redundant within the web. Injury is a much more likely cause in fact.
A physical ailment could sufficiently reduce his usefulness, but Tyson knows that there are ways to work around almost any physical disability if he had to and - as mentioned in the other headcanon - Tyson’s usefulness to the web isn’t dependant on his physicality.
An injury to Tyson’s mind or memory would be a death sentence. Tyson is useful because he is a strategist and a mathematical prodigy. He is a genius. It’s easy to forget that with the number of stupid decisions he makes, but Tyson has a genius level intellect. He had three Ph.Ds under his belt by age seventeen.
He can follow the Moriarty Mirrors logic and - almost always - match them blow for blow. There are times when they get ahead of him and times when Tyson has to break down their chain of logic much slower than they would wish, but Tyson is kept around because he can follow along if given time and can provide actual input and challenges to those ideas.
If Tyson lost his ability to learn as quickly as he does, if he lost his ability to debate - mathematics, physics, grand plans for the criminal empire - with the Moriarty Mirrors, Pup would be gone. He would still be loyal and a great guard dog, but Tyson would become any other hound at their heel.
Not their Pup. Bright, argumentative, and loyal to a fault.
Tyson would survive losing a limb. He would find a way to be useful and adapt the ways he worked if he lost the use of one of his senses. Losing his mind would break him. Not only would Tyson lose one of his few reasons for self-worth, Tyson would lose his place at the Moriarty Mirrors side. Not immediately, perhaps.
He would still have use as an attack dog and a trophy to hold over The Colonel, that no matter what Moran doesn’t get to take what is theirs. And for a time there would be a hope of Tyson recovering his memories and his mental capacities, the Moriarty Mirrors would be willing to invest in getting their Pup back, but eventually, he would be put down.
A loyal hound that had given all he had to give and deserved a painless death. Poison in one of his cups of coffee, no longer having an immunity built up and antidotes prepared from his game of trading poisoning attempts with Sunshine.