I can see the criteria for transition to a full site and I see that the site can be deleted if usage peters out. The site is certainly not petering out, so could the Powers That Be delete the site if it fails to graduate within a certain time? Alternatively, could it survive in Beta for ever?
Ultimately the decision is made by the Stack Exchange community team, though here's a little information. It can, theoretically stay in beta indefinitely if there is not enough growth to promote it, but not enough 'petering out' to close it. Essentially, growth is what determines whether a site will get promoted. I don't have sources on this because the information came from the community team.