How long does it usually take before a franchise begins making money?
The answer to this question is easy. "Who knows?"
Even in the case of a proven, viable franchise concept, if the franchisee is (for whatever reason) inept, lazy, or otherwise distracted from taking care of the business, that particular unit is probably in trouble. Now, I realize that this is not the norm, but the point, is that both the franchisor AND the franchisee are responsible for the success of an operation at the unit level.
Another point that bears mentioning, is that only around 25% of franchisors offer any type of "earnings claim" when franchising a business. This is a startling revelation to me, because it is saying that most franchisors are not terribly proud of their results.
Again, the key is "franchise due diligence" when buying a franchise, that combined with a very careful period of assessment before making the investment.