This depends on the issue being treated.
Acne scars, once resurfaced, are largely permanently remodelled. As such, you can expect to need 2 to 3 sessions of strong peels over 3 months.
Pigmentation, especially melasma, is a chronic and recurrent issue. Peels are usually combined with lasers and topical therapies and are performed once every 2 to 4 weeks, depending on the treatment plan.
Acne, too, is a chronic issue until puberty ends (sometime continuing into adulthood). Chemical peels act to control sebaceous gland activity and after an initial intensive treatment period (once every 2 weeks for 4-6 sessions), a maintenance session will be required once every 4 to 8 weeks.