If the failure can be attributed to the credit card, the Xeround account, and the authors email client, then it isn't really a single point of failure. If one (or even two) of those failed, the others should have been able to identify the problem and address it before the sites were taken offline. It was the combination of the three failing at the same time that led to the ultimate failure.
Bank of America has a feature called ShopSafe (https://www.bankofamerica.com/privacy/accounts-cards/shopsaf...) where you can create temporary numbers that redirect to your real Visa or MC account. BofA assures me that the generated number continues to work even if you lose the physical card and get a replacement.
You can use the temporary one for up to 12 recurring payments, which means you'd have to update your payment info for a bunch of services every year, and each card is only good for one merchant, so you'd need a different one for each.
It may be better to just get a separate card exclusively for recurring services to reduce the chance that it gets flagged because of travel or other suspicious activity (Christmas shopping, etc.).
Same thing happened to us, but with http://www.crashplan.com: out of the country for 2 weeks that happened to overlap with the expiry of our annual subscription. Because the credit card on file had expired, CrashPlan tried to contact us via email for a week and then deleted all of the backups!
This does seem like a key aspect of the "service" component of SaaS, in particular for cases where data is deleted or is otherwise difficult to restore (i.e. recovery involves more than just a new, valid credit card number). Maybe we need some sort of SaaS evaluation or ranking system that took these types of policies (grace periods, etc) into account...
That's really ridiculous of Xeround. 5 business days is simply not enough time to expect most people to update credit card details.
I've had similar situations with Amazon, Rackspace, etc. when my card expired, and they all gave several weeks of leeway in updating to new details, as well they should.
As an aside, this is a decent argument for a better email client. Those messages should've been highlighted instead of hiding among the chaff.