The US Department of Agriculture recommends constant refrigeration to avoid bacterial contamination and growth (salmonella). The USDA, in my opinion, is far more paranoid than is reasonable for the vast majority of consumers who have access to fresh or fairly fresh eggs (most grocery store eggs are fairly fresh). I regularly keep eggs out, unrefrigerated, for up to a week and have experienced no problems at all. Hard boiled, unshelled eggs will safely last about 1 - 2 days (probably longer) at room temperature. So, to answer your question: the USDA does not recommend unrefrigerated eggs, and my experience indicates eggs will last for at least a week unrefrigerated.