I have also noticed what appears to be a 5 day (120 hour) timer on these "weekly" quests. However, weekly maintenance seems to always reset this timer. In addition, some rolling restarts (which we've been having a lot of lately) seem to reset these timers, too. There have also been a few occasions where I've been able to do the "resource gathering" quest more than once in a 5 day period, if a different random resource is available that day.
My advice would be just to get into the habit of doing these quests on the same days each week. Do them on Tuesdays and Sundays, or on Wednesdays and Mondays. Remember that some quests are only available while on offense or defense, so you'll need to do at least two battles. Then if you happen to be in Wintergrasp other days of the week, swing by the resource quest givers to see if another quest happens to be available to you.