You don't even necessarily need the code should they pivot and do something else. You just need contracts in place for support. You need them to support you for a certain length of time and even have a stipulation that they support you for yet another length of time after they pivot or no longer have whatever version of the API it is.

That way, you'll have time to build your own. OR at that time you can negotiate buying it from them or upgrade to the latest version of their API.

No one is going to want to just give you the code should they pivot and make a new version. As a developer, I wouldn't. That's potentially trade secrets, etc. However, I would certainly sell it to you (maybe ensuring you don't resell it) should I move on and not want to support you with servers, etc.

But really, what's it take to keep a server around, with an older API version, for one paying customer? It's not as if they are losing on the deal (hopefully).

We're in the business of software here and the good thing is that there's absolutely no reason they would ever lose some version of an API. They could always go back in their revision control systems and resurrect it. So you aren't going to lose it. Not if you have an agreement. Though that agreement doesn't need to be harsh. It should be quite easy to negotiate.