DuckDuckGo pays money to Bing to use their API [1], presumably enough to outweigh any loss of revenue. DDG also uses Bing's ad network, so Bing makes money regardless of what engine a search is made on.

Also, there's speculation that Microsoft is starting to give up on getting wide adoption for Bing among consumers [2], and given Bing's low market share, Microsoft has probably determined that Bing is never going to get widely adopted enough to the point where having a deal with DDG would be a bad idea.

[1] https://help.duckduckgo.com/results/sources/ [2] https://futurism.com/the-byte/microsoft-giving-up-people-usi...