BUG #14062: pg_dump dies after dumping first 60 gigabytes of text for large table

The following bug has been logged on the website:

Bug reference: 14062
Logged by: Dan Liddell
Email address: dll(at)sonic(dot)net
PostgreSQL version: 9.4.6
Operating system: Red Hat Enterprise Linux Server release 7.2 (Maipo
Description:

For an approximately 500 gigabyte database, pg_dump dies after approximately
60 gb of text output, with an error:

pg_dump: Dumping the contents of table "datum" failed: PQgetCopyData()
failed.
pg_dump: Error message from server: SSL SYSCALL error: EOF detected
pg_dump: The command was: COPY hrrr.datum (dr_id, qtime, grid_id, gust,
ugrd80, vgrd80, pres, tmp, dpt, ugrd10, vgrd10, dswrf) TO stdout;

The command used is:
pg_dump -n hrrr --username=webuser --host=<some AWS RDS host> hrrr_db

The host is remote, and the connection is encrypted.