Is the API something that would be difficult or impossible for you to replicate on your own? If that's the case, you might have to just stick it out. There's nothing inherently wrong about building a business on top of an API, just there's a higher risk factor involved if say, the company pulls a Twitter and guts the API or goes under etc.

Otherwise, I would advise possibly building a functional clone of the API in earnest (if you have the cycles available to do so) and keep it on the backburner until needed.