How long does sepsis recovery take?

Quite variable: Depending on the severity of the initial illness, whether or not there was related organ failure (the need for a ventilator, the need for medications or devices to keep the heart and blood pressure going, the need for dialysis, etc), the nature of the infecting organism (how well they respond to antibiotics) and the health of the patient.... It could be 1-2 days or months-years.

It depends: It depends on what you mean by "recovery." the actual acute illness may take anywhere from 3-10 days to resolve on average, but can also involve ICU stays for a month or more (depending on setbacks). Even after leaving the icu, a patient will be very weak and deconditioned, and may need assistance to gain strength and ability to function independently again. That can take months of rehab.

Long time: Sepsis is a systemic illness caused by an out of control infection. Usually the doctors are very good at killing the organism that causes the infection. The problem is the damage that the infection causes to other organs like the lung, kidney, liver or even heart can take months to recover. I hope that your relative heals soon...