To use Authorize.net as a payment gateway and handle recurring donations you need to ensure the Silent Post Url is specified in your Auth.net account.
Log into your Authorize.net account,
Click the "Account" tab.
In the settings section, under the "Transaction Format Settings", click the link for "Silent Post Url".
From your RaiseDonors account, goto Account Settings - Merchant Settings - Merchant account & payment gateway (link here)
Copy the silent post url from RaiseDonors into Authorize.net
Note, if the Silent Post URL is in use for a different integration/purpose or empty, your recurring donations will still work. But, the charge from each instance of the recurring profile will not be reflected in RaiseDonors.