Hmm. when are you planting? Does it look like something is eating them from below? Are they just rotting? Do you improve the soil each year? There is a good fungicide made by greenlight call fungaway the begonia people in my area love it that and marathon.
Derick

It may be the brand you bought this time. I notice the double bloomers do great and the single bloom are easy to have issues, and more prone to perhaps a new family of slugs or other pests you may not know you now have.

Slugs and snails are my main threat.