For how long can you let dough sit there to rise without yeast?
I am not sure where you read this and it is a reasonable expectation that it would work. This is however a classic example of recipes authored by someone that worked in a certain climate, season, location and other specifics that are not always going to work everywhere else.

As already pointed out by @kettultim, natural yeast count in your environment is not something you can take for granted. It is entirely feasible for a dough to sit around for a couple of weeks, get moldy and not rise even though you had tried the exact recipe before at another time or place.

If you had it working before and you liked what you had, keeping a bit of the fermented dough and nurturing that as a starter for later use is always worthwhile.