Do you also have a wired connection to your board? If you have both WiFi and wired connections, only the wired connection will be established. If wired connection is removed the WiFi will attempt to connect. Make sure you have all the hardware connections like the Centrino N-135 and wired connection, if any, properly connected. Also, what is the password error? It might be related to the access point configuration. Take a look at this link https://software.intel.com/en-us/blogs/2014/04/25/wireless-galileo-on-yocto-linux-iot-devkit-image , make sure you have the wifi settings correctly configured and that the security settings are not blocking you from successfully connecting.
do you have antenna plugged into the adapter card? If not the signal is expected to be poor and drops would result.
Being the author of the blog you refer to: I do have Galileo running as AP stable for hours hosting 2-3 devices in my home environment.
I once also checked the setup in a faire environment with a lot of WiFi around. Here it wasn't too stable. Maybe with even better antennas I would have succeeded - at the end I moved to a Netgear AP backup solution