I can open and down load maps from my arcgis online account ... http://YZ.maps.arcgis.com/home/ to my Android tabs (Sumsung Tab 3) to use for offline data collection using Collector for ArcGIS. but, a big but, couldn’t do the same from my portal site https://www.ZY.org.et/gisZY/home .
Berhanu
For portal maps you need to tag the map as offline-ready when you save it. If you are using Esri basemaps for offline use in your portal you need to configure them for offline use.
This link Take maps offline—Collector for ArcGIS | ArcGIS has a section on taking maps offline with Portal and should help you out.
Cheers
Russ