Never let your ego get so close to your position that when your position goes, your ego goes with it.
When I read the italicized section of this quote, I had a different idea than what the description goes into. My original thought was strictly about ego, and the potential destruction of a leader when his "position" went, the ego bubble bursts and the leader loses confidence and in a manner of speaking, ability.
However, what General Powell is talking about is the need to change, which sometimes eliminates the positions that so many people rely on. People get so comfortable with what they are doing, that they forget that they need to "change with the times." The problem with this mentality is that no process is perfect, and with the every increasing pace of technology, a great process becomes good in a very short period of time. Good becomes passable, and passable becomes outright wrong. A lot of things survive on momentum, but at some point, the momentum wears down, and failure and collapse occur.
So, what are you to do? As a leader you should be looking for continuous improvement (yes it is an old business buzz phrase, but it is no less true, check out Monday's entry). General Powell states that "The proper response is to obsolete our activities before someone else does." So when you walk into work on Monday, take a look at your processes, and start figuring out how to improve, before the competition does.