In a recent interview Yu Suzuki was asked to elaborate further on what's preventing a third game from being made:
Source: Yu Suzuki Interview (Shenmue Dojo)
Fans keep providing their support on internet and even after a decade, they are still here. However, they would like to know what they could do to help you start Shenmue III's development ?
Yu Suzuki: Fans from all around the world kept providing support me and I can't thank them enough. About Shenmue, Sega is not a problem at all. For Shenmue III, we need to define a specific budget and if I can gather enough for it, Sega will allow me to do it.
I am pretty sure that Sega doesn't want to take any financial risks regarding Shenmue. That's why I have to gather the necessary budget for it. Anyway, even if I would like to work on other projects beside Shenmue, if I ever get the opportunity to work on the 3rd part, I will do it. And to be honest, I do not think that anyone else can properly accomplish Shenmue III the way I'd like to do it.
If Shenmue III's budget isn't sufficent, quality will suffer from it.
Budget and money are the main problems... If you ever reach your goal and gather enough money to create Shenmue III, do you think that you will be able to conclude the story? Knowing that Shenmue's story is very deep and seems to be far away from its conclusion.
Yu Suzuki: Yes indeed, the story is far away from being completed and to be honest, I do not think that it's possible to end it during Shenmue III. If I had to do it my way, players would experience the ending during Shenmue V. But that seems to be a lot so I'm going to try to finish it within the next 2 games.
Source: Yu Suzuki Interview (Shenmue Dojo)