bogus "No protocol specified" message

[Perry Hutchison]

When trying to open an X application on a remote display,
I am getting

    No protocol specified
    Error: cannot open display: 192.168.200.61:0

The "No protocol specified" message is bogus:  the display is
specified correctly*, and the same operation -- with exactly
the same setting of DISPLAY -- was working yesterday.  There's
no problem with network connectivity between the two systems:
ping and rlogin both work in either direction, and the specified
X server is running and accepting connections.

What does that message actually mean, and how do I fix it?

* According to the X manpage, a non-empty hostname or IP address,
  separated from the display number by a single colon, specifies
  the use of TCP/IP communication protocol.  BTW I get the same
  result using either the {ipaddress}:0 or the {name}:0 notation,
  and with or without a trailing .0; 192.168.200.61:0.0 and
  192.168.200.61:0 both fail in the same way.