In Japan here we have high humidity. Summer is ridiculous. So if edges aren't properly cared for before they are put away the edges need to have a lot taken off to get back to good condition.
My routine for summer prep has been use a middle of the line wax, not hard, not soft, wax as usual. Scrape ONLY the edges clean. Apply a rust inhibitor generously. One of the Japanese wax makers makes one in the shape of a pen that you can just run along the edges. Do it once more in the middle of summer to give the bases some juice. Come fall or early winter, get a good grind, throw some wax on it until the snow flies. Never had a problem even in such a humid climate.