Airlines don't generally have sales like that. I have heard and found to be true that fares can be lower when you purchase midweek vs. the weekend.
You can use a farewatcher site (kayak.com is one I had luck with in the past) to watch for changes in fares for a particular trip. You will get an email at what ever frequency you select with the best current fares available for your itinerary. Southwest Airlines has some DING application that will notify of special deals on your desk top but I am not too familiar with it.