How do I seal a painted deck?
Paint is a sealer of sorts. If the paint is peeling, then the issue is the paint itself. Perhaps the wood wasn't prepared right, or there is no proper primer, or they didn't use paint specifically for foot-traffic (they make paint specific for floors/stairs that wears better with foot traffic).

Your best bet is to strip what's there and start over. Sand it down a bit, use a proper primer, etc.