Trying out Collector for ArcGIS on my iPhone 5c. I was able to sign into ArcGIS.com but not my organization. When using my organization url, the Sign In page sits, spins, and never loads the username/password dialog. The default url is www.arcgis.com which works. I tried modifying the url my adding organization.maps to the beginning which fails. After several trial and error attempts I found the issue to be related to the WWW at the beginning for the url.
www.arcgis.com - works
www.organization.maps.arcgis.com - fails
organization.maps.arcgis.com - works