I have connected a Collector for iOS client to an ArcGIS Enterprise server, the Maps are coming up as expected in the gallery view. The maps are also configured for offline editing, however, when I try to take a map area offline, it asks me to login to ArcGIS Online and then errors out with a generic "Unable to download Map" error.
Any ideas on what this could be?
Which basemap have you used?
I have recently configured my maps to go offline in Collector (in ArcGIS Enterprise). Only with ESRI ArcGIS Online basemaps (registered on our GIS Enterprise) was I able to go offline.
The process is described here: https://enterprise.arcgis.com/en/portal/latest/use/take-maps-offline.htm#
Look through 'Use an Esri basemap offline' section.
The error message that you are getting implies that you might be already using basemaps from AGOL. To not get asked the password, when you registered these baseamp on your Portal, add the login details to be saved with the item (step 7 in 'Use an Esri basemap offline' section).
I hope this help, though it is a bit hard to help without knowing all the details.