I've had similar issues with PlayIt Live where it takes a "dislike" to an incoming audio source.
It will be something to do with sound card settings or setup but it can very difficult to fault find on a live system.
Reinstalling the sound card driver might be worth a try if it really won't appear to PlayIt Live. Windows 10 has widely reported sound card issues and old drivers stop working.
As a general observation, using a separate application or computer for streaming (perhaps running B.U.T.T.) or if you have the money, dedicated hardware would be my recommendation.
PlayIt Live 'listens' to whatever input you select and will stream this. If this is silent then this has not been connected up correctly. Please check the input with another software, such as Audacity. If the input works with Audacity and not with PlayIt Live then please share a screenshot of your configuration.