Hello Mike and Jane,
The reason you can't see why it wouldn't show up in a search is the problem. That is the whole essence if starting the forum here to get support as that is something that should be working. That is what they call a bug. I was able to resolve it with Airbnb yesterday after several calls.
To your next point, as stated on my listing, air beds are provided upon request:
Primary bedroom (3)
- 1 King sized bed sleeps 2
- 1 Full Size roll up bed sleep 1
Living Room (3)
- 1 Sofa that can sleep 1
- 1 Queen size air bed sleep 2
Bedroom 2 (4)
- 1 bunk bed - Sleeps 2
- 1 Queen size air bed - Sleep 2
Bedroom 3 (2)
- 1 Queen bed - Sleeps 2
Thanks.