Welcome to the dystopia your parents warned you about.
Vendor lock-in used to mean that your data was stuck in a proprietary format, requiring you to buy expensive services to migrate to another provider. With [PS]aaS, it means that your entire company can disappear in a puff of smoke if you weren't careful about your choices.
Lets figure out how to avoid that outcome.
System Administrators are a combination of maintenance staff, standing army, and consigliere. Not only do we keep things running smoothly, we guard against invaders, and we act as trusted advisors to the people who make corporate policies. It's unavoidable that at some point we will need to advise our organizations to rely on outside sources for IT services, and when we do that, the onus is on us for ensuring our company's data can out-survive the service provider we choose.
Here are some rules to take into consideration when choosing a provider:
No Roach Motel
There can never be the scenario where data checks in, but it doesn't check out. Data needs to be able to be programmatically extracted from the remote service. If raw data dumps aren't available, make sure that there's an API that can be utilized which provides a way to access all of the data that you entered, including any important metadata.
For example, I had a load balancer (actually several, because who just buys one load balancer?) that worked perfectly well. It had all kinds of interfaces to allow me to do everything I needed. I enjoyed using it because it was especially helpful with regard to generating Certificate Signing Requests (CSRs) and doing certificate management. The downside was that if you used the key that it generated to sign the CSRs, you couldn't actually export the key. It's not like it advertised that fact - it just didn't give you the option to do it. The "certificate backup and recovery" process used encrypted tarballs, and you could import into another of the company's load balancers, but you couldn't do anything else with the certificate. Talk about annoying...
Authentication, Access Control, and Accounting
You use centralized authentication to maintain your users. Use a cloud service that will allow you to automate Moves, Adds, and Changes (MACs) of accounts on their end. Also, ensure that the service uses sufficiently-finely-grained control to company resources, and ensure that when people make changes, those changes are recorded. Too many cloud providers don't offer field-level logging of data, and when a user changes a field maliciously or by accident, it can be difficult or impossible to investigate using their tools.
Do you like running email servers? Me neither. Between spam, defense from blacklisting, and half a dozen other irritants, plus the fact that our existing software of choice couldn't do the advanced calendaring that our users wanted to use led to us considering the possibility of building an Exchange infrastructure. After fully considering things, we determined that a combination of the fact that we were a primarily-Linux shop plus the license fees of building an Exchange infrastructure meant that we would be better off to outsource our email services. Because user complaints had risen to a clamor by that time, we assented to their demands and went with an affordable Exchange provider.
Unfortunately, we didn't warrant enough users to have our own dedicated server, so we were stuck in a shared environment. That also led to us having to administer our users through a broken, under-featured, over-complex web interface that had little or nothing to do with the underlying Exchange server. Plus, the company didn't support importing Active Directory users and groups, nor was there an API that would allow us to "pretend". It was a miserable experience for everyone involved.
Be Aware of Provider Limitations
Don't rely on a service provider with a lesser infrastructure than your own. A chain's only as strong as its weakest link. You use multiple AWS regions. Or maybe multiple data sites. But a bad choice of a SaaS provider can ruin all of your carefully laid plans. Investigate and decide accordingly.
You know exactly how much work and effort you spent on developing a solid, stable infrastructure. You know that you have disaster recovery plans, and that you test your fail saves and fail overs. You don't know about the SaaS provider's infrastructure until you ask. One of the first things I did with companies I was evaluating for hosted services was have an in-depth discussion with an engineer from their side who could talk with me about things like infrastructure and service uptime, SLAs, and so on.
Essentially, I interviewed the companies like I interviewed potential employees, because there are a lot of similarities. Both are working for you, both can screw up and cost you uptime, and firing both is harder than you'd like it to be. On the other hand, the right company (and the right employee) can both make your life immeasurably easier, too. Good service is rare, so when you find it, treasure it.