I have experienced the same issue. First time the solution was to remove domains for editor tracking fields (creator and editor fields). However, I run into same issue today and editor tracking was disabled, so there couldn't be an issue with editor tracking.
After investigating further, I have found out that one of the fields which had a domain assigned, contained values which were not present in the domain. Once I have removed the domain from the field, I was able to see related features in new Collector for ArcGIS.
Without any further testing, it seems that related data cannot be accessed from Collector, when there is a domain assign to a field, but some values in the field are not present in that domain. In any case, I would recommend to remove all the domains from the related table, republish the service and see what happens. If it works, you can start to add domain one by one and see which causes the issue.
Generally, it could be said, that the domains are causing lot of issues in new Collector for ArcGIS. So anytime I have problems, I am trying to remove the domains, and in most cases, I find a domain which causes issues with the map.