I was experiencing the same problem, after we changed from sandbox to production with an updated web design. The site already used Braintree successfully in the past.
After talking with Braintree, we realized the transaction was failing because it was not receiving the required zip code and email address with the transaction details from Gravity Forms. I did have a required billing address and required email in my form, but the Braintree plugin is not passing those details with it.
We had to temporarily disable the AVS “zip code not included” rejection in Braintree Settings, and also disable the default Email Receipt option.
I will probably have to add some custom web hooks or create a custom module to get this working properly. I attempted to visit the developer’s website and it has a security warning and will not display.
Best case scenario, the developer for this Braintree plugin should update it to include options for the billing address fields and email address fields.