The fares indicated in the alert email won't available through booking sites for several hours after the altert is sent. So if you click on the link and immediately try to book a ticket, the fare in question probably won't be loaded yet.

I generally fly Delta, who always seem to be last to lower their fares in the markets I watch. So things generally unfold like this:
1) FareCompare email alert arrives with a new fare from a competitor.
2) Four to 24 hours later, Delta matches above fare, but there's no email from FareCompare since the price isn't any lower than step #1. Just have to keep an eye on the cities in question.
3) Two to six hours after step #2, Delta's new price is available on purchasing sites.