Can you point to any SaaS best practices in this area?That's surprisingly difficult. IMNSHO, most SaaS fails completely on this count, and my businesses use very few of the trendy services for exactly this reason. Of those we do use, every single one is either (a) convenient but expendable without compromising the business, or (b) both well established and having some form of legally binding statements along the lines below.
What I would ideally like to see in most cases would be a guarantee that if a service were to be taken down then its source code would be released with some form of open licence so that any service you relied on could reasonably easily be converted to self-hosting. Obviously this isn't worth much for services that are essentially proxies, such as most payment services, but it's sufficient for continuity in many cases.
Otherwise, as a minimum I'd like to see automated tools for exporting data in some open format so it can be transferred to an alternative platform where this is a reasonable possibility. Where there are non-trivial issues relating to data export, such as with PCI DSS for the various card payment services, I think the most plausible approximation would be a legally binding promise to help transfer the data to an alternative provider.
Obviously if a start-up fails suddenly then even legally actionable promises aren't going to be worth much if anything, which is why we won't rely on any SaaS from a new start-up for anything essential no matter what their terms say. However, properly worded guarantees would at least stop exit strategies like acqui-hire or sell-to-competitor-who-shuts-you-down from screwing the customer base.
One good example IMHO is MailChimp, which provides a straightforward mechanism for customers to back up all their important data, not just mailing lists but also things like e-mail templates and stats that normally live on the remote system.
Another one that seems reasonable is Stripe, which has explicit wording in its (UK) legal terms guaranteeing meaningful notice under fair conditions if they're going to terminate an account, and guaranteeing that they will facilitate transfer of card data to another payment service also under reasonable conditions if a merchant using their service decides to terminate.