I want to point one thing out with the question itself. The Scrum Master is by no means responsible for actually maintaining a burn down. The team is responsible for coming up with a plan for delivering on the stories chosen for the sprint. They may well use a burndown as part of that plan, but the team is responsible for it happening.
There is certainly a balance. The team and more importantly the Product Owner will know through the inability to forecast effectively (yes we forecast) when they are not grooming the backlog often enough/effectively. Adjust.
A Scrum Master can and should remind the team of their duties of transparency and coach the organization that, yes they are right in asking for forecasts from the product owner. The Scrum Master is not responsible for and should not /make/ the team do these things. [S]he is not a project manager.
When the team has an appropriate forecast of a few months out or enough to guide the rest of the organization, you probably have enough. There is no right answer though.