My kitchen cabinets are peeling

When we did our renovation, we spent a lot on the appliances but went light on the cabinetry - we used veneered ones that were maybe a little better than Ikea.  Well, predictably, five years later, the appliances are working great but the veneer is starting to peel in places, particularly on the drawers and cupboards near the oven that get pretty hot.  What are the options for changing the cabinetry at this point (we have a lovely granite counter top that I don't want to replace) and how much will it cost?     My mother-in-law had a new veneer put on her cupboards about 10-15 years ago but I never thought it looked that great to begin with and it didn't hold up that long.