ITA can do exactly that over a period of a month ("Month-long search"). It works great, as you can specify airlines, routings, booking classes, etc using their syntax, but the drawback of course is that you can't actually buy tickets, though you can normally replicate the findings on sites like Orbitz, etc.

If you're a Firefox user, there are some greasemonkey scripts around (created by a FTer) which further extend the options in the month-long ITA search.