For a more neutral approach I would choose agotarse or desgastarse, though strictly the first one is the step before quemarse and the latter is more like getting exhausted.
For us quemarse means loosing all standing in a post or profession as a consequence of blunders or malfeasance. We rather use fundirse for burning out (it comes from melting your car's engine for keeping it at top revs during a whole hour in a sort of hollywood car chase, or failing to notice the coolant hose is broken).
As for burnout, it depends on the meaning. We have several words for those who get their brains like Gruyère because of the drug abuse, but for the general meaning you may use desgastado.
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