It was true every year from 1945 through 2000; the D'backs broke it with four (Luis Gonzalez, Mark Grace, Miguel Batista and Mike Morgan). The 1960 Pirates also had three, but Ron Berler, who came up with this (admittedly somewhat silly) theory, said that Don Hoak had "renounced" his Cubness, hated every moment of his single season as a Cub, and that got that year's Pirates team off the hook.
Whether you believe in this or not, let's have a look at each of the eight teams remaining in the 2012 postseason tournament and where they stand as to ex-Cubs (note -- former Cubs minor leaguers don't count; the player has to have been a major-league Cub to qualify):
Nationals: 2 (Tom Gorzelanny and Mark DeRosa, though it's not yet clear whether DeRosa will be active)
Giants: 2 (Angel Pagan, Xavier Nady)
Reds: 2 (Sean Marshall, Miguel Cairo)
Tigers: 0 (no, Omar Infante doesn't count -- never played a game as a Cub)
Yankees: 2 (Clay Rapada and Casey McGehee; again, not clear if McGehee will make their active roster. Rapada faced exactly one hitter as a Cub.)
So, this season, there aren't many former Cubs in the postseason at all, just eight possibilities, spread out among four of the teams. That, I'm thinking, says something.