So after some exhaustive consultations with Airbnb, there is an ongoing problem with host properties not appearing in search results due to one particular factor, namely, your location/address isn't adequately affixed the correct coordinates in the mapping configuration utilized by Airbnb to assign your listing a specific locality.
If you believe your home isn't appearing, you MUST contact Airbnb DIRECTLY and advise them of your precise GPS coordinates (this does NOT mean your address, phone number, Airbnb URL, mother's maiden name, etc.)
Here's how you obtain your GPS coord's from Google:
https://support.google.com/maps/answer/18539?co=GENIE.Platform%3DDesktop&hl=en (IMPORTANT: Follow the instructions for " Get the coordinates of a place".)
For iOS, it's MUCH more complicated, so I suggest you use Chrome instead and use the Maps feature. But if you're a confident Mac power-user, here's how:
http://www.leancrew.com/all-this/2014/07/extracting-coordinates-from-apple-maps/
N.B. This may NOT solve all your search criteria, but it may very well be part of the remedy - it worked for me 🙂