A business without any capital investments (tools, inventory, human capital, your "rainy-day fund") isn't much of a business at all. As long as you're tying up capital in the business you need to justify that investment by turning an accounting profit; otherwise the business is
losing money compared to what could have been earned by investing the same resources in some other venture.
Economic profit, which factors in opportunity cost, does tend toward zero. A sustainable business can exist with no economic profit or loss, but the accounting profits would be in line with standard market rates of return.
Of course, if the business's investors are also its employees (as is often the case for small, privately-held businesses) then any accounting profits can be distributed in the form of salaries... but in that case the investor-employees will expect higher salaries than they would receive as mere employees elsewhere.
Keeping up with inflation does not count as growth. Growth or decline should be calculated in terms of purchasing power (inflation-adjusted dollars), not raw currency.