After some additional testing with a new MXD and with the old MXD, it looks like the root cause of my problem was the data frame projection. In the old MXD I had reset the projection to Web Mercator late last week because I was testing some projection related issues with uploaded the trace results to a hosted feature layer which is in Web Mercator.
In the new MXD if I change the data frame projection to something other than the data source projection, the placement of the flags and barriers fails.
In the old MXD if I change the data frame projection back to the data source projection, the placement of the flags and barriers works.
From Tom:
After some additional testing with a new MXD and with the old MXD, it looks like the root cause of my problem was the data frame projection. In the old MXD I had reset the projection to Web Mercator late last week because I was testing some projection related issues with uploaded the trace results to a hosted feature layer which is in Web Mercator.
In the new MXD if I change the data frame projection to something other than the data source projection, the placement of the flags and barriers fails. In the old MXD if I change the data frame projection back to the data source projection, the placement of the flags and barriers works.