Burnout is the result of too much demand versus too little capacity. The primary way to combat burnout is through prioritization. The Product Owner is responsible for prioritization.
When items are not prioritized appropriately, the team has to juggle and multitask. They burn out.
The other role that protects the team from burnout is the Scrum Master. The Scrum Master manages capacity. A capacity management session before the Sprint is essential. This allows for the team to not over commit to the items that they will be delivering for the Sprint goal.
So, the next time your team is feeling burned out, look at your prioritization and ensure they have the proper capacity calculated so that they don't over commit.