I read this in John Avlon's May 12th column in The Daily Beast: “A more accurate means of measuring listeners showed that conservative talkers’ ratings had either declined or flatlined in the heat of the 2010 election. . . .”
To me, the verb "flatline" means "die" and is derived from the straight line displayed on an emergency-room monitor attached to a patient who has expired. Avlon was using it in the sense "hold steady."
So I checked with Oxford English Dictionary and discovered that both meanings are valid. Avlon's sense is derived from the line on a graph which neither rises nor falls, but remains steady. The meaning I was thinking of refers to a sudden drop to nothingness.
Unfortunately, these two incompatible meanings emerged at roughly the same time. According to the OED the first published use of the “hold steady” meaning occurred in 1976, and the first use of the second meaning in 1980, where William Safire commented on it in his “On Language” column in the New York Times.
So now we have a common term which can be very confusing if the context doesn't make clear which meaning is meant. That’s something for writers to keep in mind.