What are the chances that the Ubuntu Project will die if its primary source of funds are removed? In other words, how healthy are the finances of the Ubuntu sponsors Canonical? Is Ubuntu losing money?
There are two things to understand to answer your question :
first, Canonical is backing Ubuntu. Not Mark Shutleworth. What I mean there is that Canonical is a commercial company that sells services (training, support, customizations for OEM...). Last time I heard from them, they were making some money, not enough to be profitable, but they are not crashing either.
second, Mark Shuttleworth created the "Ubuntu Fundation", an association whose purpose is to fund the Ubuntu development/support, if Canonical fails. The Fundation has 10M$ in cash, and is doing nothing with it (well, I guess they have placed the money somewhere, but that's not the purpose). It is in a "dormant" state, and will be activated if Canonical cannot support Ubuntu anymore. If it is ever activated, it will pay the Ubuntu developer to continue their job, as long as possible, and at the minimum until the existing Ubuntu release reaches their respective end of life.
The important point here is that neither Ubuntu, Canonical, nor the Ubuntu Fundation are dependant on Mark Shuttleworth's money. He already gave some of it to those institutions, and now they own it... So even if Mark Shuttleworth spends all his millions, Ubuntu should stay in good shape.
Mark Shuttleworth started an Ubuntu Foundation with an initial funding committment of $10m. This trust that has the purpose of giving Ubuntu continuity should Canonical ever be dissolved.
The funding is sufficient to 'meet the public commitments to keep Ubuntu entirely free of charge, as well as meeting commitments of support for extended periods."