Wikipedia disagrees about the profits on "most of its flights". It says
"it is reported that British Airways then ran Concorde at a profit, unlike their French counterpart". That is half the fleet for slightly over half the years of operation.
The linked-to http://news.bbc.co.uk/2/hi/business/2935337 says:
"British Airways […] was reckoned to make a £20m annual operating profit from its London-New York Concorde service."
But also:
"By 1975, the year before commercial launch, more than £1.2bn - at least £11bn today - had been spent."
So, their margin on investment was 1.6% or so, starting about ten years after the investments were made.
They would have needed a lot more planes to get their investments back. To fill them with passengers, fares would have to drop. Lower fares means they needed even more planes, etc.
Concorde also was limited to long distance flights. On shorter routes, its fuel economy did not compensate for a slightly shorter (boarding+flight+deboarding) time.