Everyone's giving different answers, which is not surprising. We all have different strategies for coping with unendurable burdens.
My strategy is sheer bloodymindedness, but I find I can only dredge that up so often. When I push through burnout when I know I shouldn't, I end up knackered for months.
It's an effort I can really only dredge up once a year or so. Make sure you talk to your boss about this.