Early in the game the expected value of a trip around the board is positive because of low rents of undeveloped properties and the net gain from Chance and Community Chest, plus passing Go. Cash flow into the game is positive as a whole.
Later in the game, when property is developed you're going to be paying bigger rents. This is going to cause players to mortgage or sell houses to pay the big rents (also their own liquid cash supply is likely lower from developing their own properties), each of which is a money sink since you don't get full value for these. This causes money to exit the game, eventually leading toward bankruptcy.
However, this requires that players actually get to develop their properties. If the game hits a lock due to no one trading and no one getting a natural monopoly, the game can go pretty much indefinitely.