I recreated the service to the minimal level to prove the concept to myself. Then I worked backwards reversing the changes until it stopped working again.
For what it's worth, here are the changes I made:
1) Moved the feature service to the root directory of my ArcGIS Server
2) Removed the requirement for HTTPS and a login to the feature service
3) Used a "publisher" account in AGOL (had been using an admin account)
4) Removed all fields save a couple of text fields
At this point, it was working great.
- I added more fields back, and ultimately all fields back. Still working great
- I tried the admin account. Still working great
- returned the service to the secure folder, but with the permissions on the feature service itself wide open. Still working great
- Changed the security settings on the Feature Service to allow access to all users who are logged in. Crashes when trying to open the feature popup.
The Feature Service works fine for editing in AGOL.
So there seems to be some problem with editing related tables using secure feature services using the Collector App.
EDIT: I created a feature layer in AGOL referencing the Feature Service in ArcGIS Server with saved credentials. Then I set the map to use the feature layer instead of the feature service directly. Now editing works on the secure service in ArcGIS Collector App for Android. So that's a work around, though not ideal.