Thanks for writing. It sounds like for some reason river birch isn't a good choice for your area. Perhaps the soil is too alkaline or there's a nutrient imbalance holding it back? Or perhaps you have pests such as birch borers in your area that really like it? Unfortunately, without being able to see it in person and know more about the growing conditions, I can't say why you're having trouble with the trees.
Since you've had bad luck twice now, I'd really look at another plant. You might look into something like a paperbark maple, which has a similar peeling effect on the trunk.
---Justin, Senior Garden Editor, BHG.com