I just discovered that Filemaker is a culprit in the inconsistent behavior. The layout the web page uses will sometimes display all the related addresses and sometimes only some. In table view, that layout was not displaying some addresses so I did a Records->Refresh Window and the addresses all appeared.
I am adding a Refresh Window with Flush Cached Joins script trigger onRecordLoad. I'll watch for a while and report back here as to whether that does the trick.