Check Often. Really Often.
It can seem pretty random, but there are at least a couple of guidelines airlines have to follow regarding price changes, thanks to the Airline Tariff Publishing Company (ATPCO). During the week, they can update their domestic fares up to four times a day; during the weekend, they can update them once a day [source: ATPCO]. International fares can be changed more often, but typically aren't [source: Hobica].
Of course, you don't know exactly when those changes are going to happen, and you might wake up on Tuesday to find the flight you want is $100 less than it was when you went to sleep on Monday night, and by lunch it's $150 more.
So check often -- at least every day, preferably several times a day, and, absurdly but ideally, every hour.
Of course, doing a route search every hour might be impossible (and your supervisor may strongly object). Luckily, there is an easier way to go.