How long would someone be on immunosuppression meds after a transplant?

For the organ's life. The transplanted organ will never change its genetic identity - it will always be made of different dna than you. Your immune system will ultimately recover from the drugs you took, recognize the organ as "foreign" and reject it. Although a very small percentage of people can get away without taking the meds, we cannot predict who. For this reason, you must plan to take them forever.
Usually life long. Most transplant recipients need to be on immunosuppresive medication for the rest of their lives. In a small number, microchimerism may induce tolerance and allow the person to get off medication.

Related Questions

How long would someone be on immunosuppression meds after kidney transplant?

For life. A successful transplant can have the dose of drugs reduced over time, perhaps some of them discontinued, but even the best matched organs will need continued immunosupression. Identical twin transplants, which are rare may be an exception. Read more...
Forever. If you stop immunosuppression the kidney will reject. Therefore you will need to stay on medication indefinitely. Read more...
Life long. Some immmunospression is needed as long as the graft is working. Read more...