What is the maximum duration for a patient to be on immune suppressive medication?

Depends...: It really depends on the condition being treated. These medications are used life-long for transplant patients but can vary for autoimmune diseases such as rheumatoid arthritis or lupus.

Meds exist <50yrs !: Suppression of the immune system with various drugs was really only developed in the 1960's and after. So, few patients have been on these types of drugs for more than 40 yrs. But there is no specific clock that limits their use. As with any medication, use balances the good hoped for, with the bad it might cause. For txp recipients, there is no alternative since organ loss = death (or dailysis).

For life: Although it could be reduced, tapered, or stopped, immunosuppressive medications if required should be used for life.

Lifetime: Almost all organ recipients take their medicines for the rest of their lives, as long as their organs are functioning.

No absolute time: There have been transplant recipients taking anti-rejection medicines for as long as 40 years. With time the risks of developing infections and cancers increase. Skin cancers such as squamous cell and basal cell tumors are not uncommon after 20 years of continuous immunosuppression. Especially, in patients with prior heavy sun exposure.