If you are changing your nonprofit bank account you'll need to contact the following entities to ensure your credit card processing is not interrupted.  

1. Your merchant account provider

They control your deposits and can reroute them to a new bank account. 

What is a merchant account?

2. Authorize.net

You are probably being billed by them through your bank account. You'll need to log in and update your billing info.

How to update your billing information

What is Authorize.net?