Is it really Google's responsibility though? You'll already be getting emails from your registrar telling you that the domain is about to expire. And it isn't just Google, any service that is linked to another account/service in this way would be vulnerable, so the headline should be "don't let X expire while you have important stuff in Y that can be accessed through it".

That said, a warning message on login would be nice. They could check the whois records on initial registration to see when the domain is due to expire, and verify that (in case it has been extended) before giving a warning.

There is an easy way to detect a domain expiring that would stop accidental access to data like this by new domain owners. IIRC on signup for Google's apps you add a TXT record to the domain to prove that you control it - if a domain is expired and renewed by someone else then this TXT record will be gone. Again there is no need to check on every login, just when the domain is due to have expired. Of course this does not protect against intentional access, as the TXT record could be remembered and re-entered by the attacker if they are registering the name specifically to get access to the data on accounts like Google apps.