You can get notice when a client has been suspended (unsubscribed) due to billing failure on the Notifications/Custom Fields page of each offer.
Do this by checking an alert email for "Cancellations, Suspensions and when Podcast/RSS Feed is Paused due to max load limit" (and supply an email address for that alert email).
Note that this will NOT alert you to billing failures before the client is suspended.
You also have the option of getting alert emails for all events of all clients and all offers.
Do this from your preferences page, found from the main menu under My Account >> Profile & Preferences.
In the Notification Settings section, check the option "Notify admin email addresses of ALL subscriber activity".
However, if you have a lot of volume running through your account, this may also be high volume of email.
Another method to be alerted when a billing failure happens before a client is unsubscribed, is to use the outgoing API. Do this on the Notifications/Custom Fields page of each offer.
The basic approach would be to create a custom script on your site that is set to watch for events with mode=decline.
This mode is triggered in the API when a client payment is declined, but has not yet been suspended (unsubscribed).
Point the outgoing API URL to your script, and have your script take some action, such as emailing you an alert, when it receives an API call with mode decline.
You can find documentation on the use of the outgoing API here:
To find clients currently unsubscribed due to billing issues, do a client search.
From the main menu under Manage >> Clients, select the Subscriber Status as 'Unsubscribed' and the Reason For Unsubscribe as 'Automatic Re-Bill Failed'. (For Cancellations, do another client search using 'Client clicked Cancel Link' as the Unsubscribe reason.)
You can further filter it by individual offers, if desired, or by date range of their unsubscribe date, or both.
The resulting client list will show you clients who have been unsubscribed due to billing failure.
As the reasons for a billing failure will vary, you will need to look at the transactions for individual clients to see what might have caused the billing failure.
From the client search list, click 'Edit' by the name of each client. In the client record, you will find a link to view their billing history.
In the billing history, you should find the failed transaction record.
Clicking into the individual transaction record will show you the details of the transaction, including the reason codes for the decline/failure.