Ok, so the upshot of the support ticket was that this is a known bug -
http://support.esri.com/bugs/nimbus/QlVHLTAwMDA5ODI2Mw== (2016)
and I think I'm also seeing this in the case where none of the layers in my feature service load when using "Add Data from ArcGIS Online", or something like it,
NIM104467: Multiple feature classes published as a hosted featu.. (2014)
And there is a thread about it here.
Only see layer 0 in ArcMap when adding data from ArcGIS Online. BUG??
The work around I'm using is to create .lyr files for these multilayer services, or create .mdx files with the layers already in them so that other users can access and edit this data without having to use “Add Data from ArcGIS Online” in ArcMap. Another suggestion from the thread was to use the "Open in ArcGIS Desktop" option for a Web map in ArcGIS Online and then distribute the downloaded .pkinfo file - I wouldn't have been keen on this solution for various reasons, but this only seems to work in the case when I only get the first layer of the service loading, in the other case, where no layers load from "Add Data from ArcGIS Online" at all, the .pkinfo method doesn't work (whereas .lyr and .mdx files do). Different but perhaps related bugs...?
EDIT: Just to add another gotcha if you go down the .mdx route to share view/edit access with other users to your multilayer services on AGOL, if they don't load properly in ArcMap using “Add Data from ArcGIS Online”. In both ArcMap 10.2.2 and 10.5, if I use such an .mdx as a template (New), again, only the first layer loads, the others don't connect . However, if I open the same .mdx directly (Open) then they all work fine.