It depends on the number of players in the tournament and the time-out setting. The more players there are, and the greater the TO period, the longer the tournament will last.
The longest tournament I know of, and which is still going on, is 'One Hundred to One'. It has 100 players (obviously!) and a 7 day TO. It started in November 2002 and the second round is nearly complete. With one more round after that, I expect the tournament will be over by the spring of 2004. So it should last a total of about 18 months.
The Bird Theme tournament has 156 players, and a 7 Day TO. With the same TO setting as '100-1', but with 50% more players, it's reasonable to assume it will last 50% longer.
So my guess is it will last at least 2 years.