I have a bukkit plugin (minecraft) that requires a connection to the database.
Should a database connection stay open all the time, or be opened and closed when nee
Actually, it's all matter on how you write your application! It's an art, but sadly everyone takes a tutorial for a good practice like Microsoft's tutorials.
If you know what you are coding, then you keep your connection open for the lifetime of the application. It's simple, not because you have to go at work in the morning that everyday we have to build a special route just for you! You take that single route or 2 or 4 like everyone does! You judge for the traffics and you build 2, 4 or 6 routes as needed. If there is traffic with these 4 or 6 routes, you wait!
Happy coding.