My refrigerator stops cooling, can you help me diagnose?

I have a Kenmore 596.71102101 bottom freezer unit. I have had it for almost 13 years. Over the past 6 months, the refrigerator won’t be cold enough. The freezer will be frosted over with ice. If I unplug the refrigerator and defrost the freezer for a day or so and plug it back in, it works fine.
My assumption is that the freezer gasket needs replacing but I would prefer to hear from someone with more experience.