We see a few queries, in Blogger Help Forum: How Do I?, about domain registration renewal.
How do I make sure my registration gets renewed?or
How do I renew registration before it expires?or, possibly
My blog now displays a search page! Have I been hacked?
Some registration issues will depend upon how the domain registration was originally purchased.
Domains purchased directly from a registrar - whether using eNom, GoDaddy, or a third party registrar, will have to be renewed directly from the registrar. It's not possible to migrate a direct purchase to Blogger / Google registration for payment, any more than to use the Blogger / Google automatic DNS setup. Once you purchase domain registration from a registrar, you are on your own.
If you used Blogger "Buy a domain", Google Apps, or Google Wallet, to purchase the domain registration, you should get email reminders when registration is expiring. However, this will depend upon whether your Blogger / Google account, under which you purchased the registration, uses an active and accessible email address.
If you choose to anonymise yourself by using a bogus or inactive email address for your Blogger or Google activities, don't expect to get email reminding you, or allowing you to renew domain registration.
The most reliable way to assure the domain remains registered is to use domain auto renewal. You can check your auto renewal settings using the Google Apps administrator account, for the domain (now called the "Admin Console"). Be aware of the oddities of the Google One Login wizard, and Google Apps, when logging in.
For domains purchased before December 2012, you'll use email from Google Apps, or an entry in your Google Wallet log, to retrieve the token to setup your Google Apps account. For domains purchased after November 2012, you will have only a limited access Google Apps account, which you should reset the password, to access.
If you intend to use domain auto renewal, make sure that the bank account (credit, or debit) is active, and currently paid. If your bank rejects the payment, you should get a notice - but again, this will come reliably when the email account associated with the domain is active and accessible by you.
Procedures for renewal after expiration are different - and may cost substantially more than the normal yearly fee.
The best renewal experiences, of course, start with advance planning.