For anybody that may be struggling with this, the Nexus 5x and the Pixel C with the Android Nougat (7.1.1) update appears to have a bug, whereby once the wifi connection restarts, proxying the connection will not work.
To get the proxy to work, at least when debugging your apps....
Set the proxy & port on on the active wifi connection AND DO NOT restart your wifi connection. This appears to work for as long as your wifi connection is not dropped.
Once wifi is restarted (either manually, out of range, whatever) - the proxying doesn't work anymore despite the settings persisting. To get it working again...
1) remove proxy settings
2) restart wifi
3) add proxy settings AND AGAIN, DO NOT restart wifi connection afterwards.
Hopefully, this will help someone avoid this issue.