Refrigerated mayo will stay more fresh and will last longer. Since commercial mayo is oil-based, my guess is that it could go rancid much more quickly, especially if the cupboard is warm. Also, food particles left in the mayo can go bad, so you'd have to practice extreme caution when using utensils. I'll still keep my mayo in the fridge, but I won't worry about mayo packets or occassionally forgetting to put the mayo back in the fridge.
YMMV. Viewer discretion is advised.