If a recurring donation charge is declined you should get an email notification letting you know, and as well it will show up under the Recurring Donors > Failed Payments section.
When a payment fails Stripe will try again 3 times over the course of the next week. However, if you know the credit card needs to be updated you can also update it from the Failed Payments section in the app. You'll just need to contact the donor to get the updated card number, or expiration date. They're contact info will be listed there if you need to get a hold of them.