How long can I keep unleavened dough at room temperature?

Can a dough of only flour and water stay usable indefinitely (as in between a few days and a few weeks) when stored covered at room temperature?

I made a batch of dough last week and ended up with a good portion of it unused. Today, I finally managed to finish it off by turning it into flatbread. Having the dough on hand throughout the week was convenient, but is there anything that I should watch out for in terms of food safety or taste?