As long as the Buckeyes are stored in an airtight contain in the refrigerator then the Buckeyes will keep for around 2 weeks before going stale or bad.
Usually you or someone else will eat the Buckeyes way before 2 weeks since they're so delicious.
I can never keep Buckeyes in the refrigerator for longer than a couple before either I eat them or someone else in the house eats them.