Certified GKH Gardening Expert
It may be over-harvested. Over-harvested rhubarb is far more susceptible to pests and disease. You may need to let it sit for a year and not harvest to let it really establish so it is harder to over harvest it.
But, for this immediate situation, it sounds like a fungus is attacking it after the harvest - so you can try treating it with a fungicide. Neem oil is a good choice as it is organic and safe for consumption.