I had the same problem like dangermouse. My Volumio (on RPi3 with in-built WiFi, fresh SD image, Volumio v2.296, No DAC attached) always showed a lot of available WiFi networks around me but never my own one and also manual WiFi configuration was ignored. LAN was always working. I tried a lot of things but finally I obviously found the root cause (at least for my setup)
My router is an AVM Fritz!Box with WiFi currently running on standard 2.4 GHz, 802.11n+g+b, WPA2 encryption and using automatic channel selection incl. channels 12/13 (to minimize interference with neighbour networks). The typically selected and active main channel was 13 (2,472 GHz) so far. In this setup the Pi with Volumio was never able to see my WiFi.
Then I deactivated the automatic channel selection and selected channel 1 or 6 as a fixed setting. In this setup suddenly my home WiFi became visible and I was able to select and succesfully attach to it. In a next step I activated again the automatic channel selection (without the channel 12/13 option) and this was still working! (active main channel was also in this mode either 1 or 6).
When I then activated again the channel 12/13 option and triggered a new channel selection that led to a setting of channel 13 as main active, then Volumio lost the connection and enabled the internal hotspot instead (without further recovery).
=> My conclusion: Either Volumio or the Pi3 in general (I haven’t tried another distro on it yet) does have a problem with this high WiFi channel 13! So try to avoid them and you may have better success
And keep in mind if you play around with your WiFi router settings to test this behaviour: After applying a change you may need to restart the Volumio WiFi network as well (either via the network menu while connected to the internal hotspot or by a full reboot).
I hope this helps some of you who have similar problems.