Can One Sponsor Sustain a FOSS Project on the Long Term?

These days I am receiving quite a number of mails that ask the same question: If a FOSS project is sponsored by only one company or entity, do you think it’s a healthy project?
 
In order to answer this question, we need to define some terms first. Let’s start by the term “sponsor”. By sponsor we mean an entity (company, NGO, Government) that provides certain types of resources. We can think of resources as roughly falling into three categories: infrastructure (website, tools, etc.), contributors (developers, engineers) and funding. Of course by providing infrastructure and contributors, the sponsor provides funding indirectly as well. But if we break the notion of sponsoring into these three different kinds of resources investment and sharing, we can already see that the answer is not as straightforward as it may have seem at first sight.