There is the possibility that as you continue your project, something that looks at the time to be a thing that you'll only need one of will suddenly turn into something you need more of down the road. In games, one of the easiest examples would be that of a player. When starting the game, you may think you're only going to have one player, but maybe later you decide to add co-op. Depending on what you did before, that can be a small or huge change to the project.

Finally, one of the more common mistakes we see once programmers learn about Singletons, is to create managers for everything, and then make the managers all Singletons.