They may be more comfortable with this kind of thing if they start allowing trusted employees to do some of their work remotely. The reason is that, rather than take that time off completely, you can just make up the hours at a time when you are feeling better at home. You could even offer to track your time in a way they can see it. That could also help if the reason you are burning out is because you already put in extra hours somewhere, then you should be able to take off early at some point without having to make it up.
The remote option is a fine especially when you have already built trust with your team and the management.
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