How long can you live if you don't treat sepsis?

Few hours: Few hours, sometimes a few days.

Very individual: Depending on how severe the infection is, some may be self-limited, but most progress without treatment, particularly in older people or those with pre-exiting medical conditions. So it is hard to say exactly how long but why would you not want to treat it? Treatment is usually antibiotics, IV fluids etc supportive care, nothing fancy or controversial.