Okay, I verified the map is not set to offline. I checked in the portal item properties, is there another location to check? You said "On the device" but I'm not sure where I look for that. I suspect as the map is not offline enabled, the option to go offline doesn't exist.
The feature services in the map are "real" urls (fqdn's) and not localhost.
It is a new map for the 10.3 services, the basemap is actually a 10.3 service and works fine. In fact, if I understand the documentation correctly, I should even see the map listed in Collector on the iOS device if Collector didn't recognize that it had editable layers.
Finally, I have also enabled versioning and that does not work either.