After the Bing Webmaster Tools API stopped working almost a month ago, Bing said on their blog that they fixed it. They said "upon investigation, we discovered a technical glitch which led to API call failure that is now resolved."
I am not sure why it took Bing so long to figure out there was an issue. Bing said "we are very grateful to you, our users, who brought this to our attention and thank you for your continued feedback and support." They added:
Bing and Bing Webmaster Tools are actively listening to you and we value your feedback. It’s important to how we continually improve Bing and to help notify us of potential issues. It’s easy to provide feedback: just look for the Feedback button or link at the bottom of each page. It’s in the footer or the lower-right corner and it looks something like this:
So I guess now you can start using the Bing Webmaster Tools API once again.
Forum discussion at Twitter.