I haven't flown with Peach, but from what I understand they are more reliable than the other Japanese LCCs (AirAsia and Jetstar), mainly because they are based at KIX which is less crowded than NRT and doesn't have a curfew. That said, they still have a couple of basic reliability problems in comparison to JAL: no backup/reserve planes and very tight schedules with short turnarounds. I recall that they had a lot of maintenance and operational issues around the time that they started out, but it seems like things have stabilized as of late. Still, I'd say there is definitely a greater chance of a long delay with them as opposed to with a legacy carrier.

They don't interline with anyone, so if there is a long delay or cancellation, you either have to wait for their next available flight, or get a refund and buy a last-minute ticket with someone else. Also, in case you aren't aware, Peach has really tight seat pitch, more or less like Ryanair's (but the same as Jetstar's A320s, I believe).