Advice to travel in a particular month ages badly. The cheapest weeks move from year to year because the things that create demand peaks are themselves movable.
School calendars redraw the peaks
Family travel is concentrated into school holidays, and those dates are set regionally rather than nationally in many countries.
Staggered breaks mean the peak rolls across several weeks, and which week is worst depends on which populous region is off at the time.
Because education authorities adjust term dates periodically, the same calendar week can be peak one year and shoulder the next.
The rotation is sometimes deliberate policy, with regions taking turns at the earliest slot so that no area always gets the same weeks, which moves the peak by design.
Movable festivals drag demand with them
Major religious observances that follow lunar or computed calendars shift by days or weeks, and travel demand moves with them.
The effect extends well beyond the destination where the festival is observed, because diaspora travel fills routes in both directions.
A week that was cheap last year can therefore sit directly against a festival this year without anything else having changed.
Airline capacity decisions move independently
Airlines set seasonal schedules months ahead based on forecast demand, and they add or withdraw capacity route by route.
A route that gains a competitor sees fares fall across the whole season, while a route that loses one sees the opposite regardless of demand.
Aircraft are also redeployed between markets seasonally, so capacity on a given route can change even when the airline's total fleet does not.
A larger aircraft on the same route has the same effect as a new competitor, because the additional seats have to be sold at whatever price clears them.
Weather-driven demand shifts too
Ski and beach seasons are sold against expected conditions, and operators adjust their season lengths as those expectations change.
Shoulder periods lengthen or shorten accordingly, which moves the boundary between peak and off-peak pricing.
Events with weather dependency, such as bloom seasons and wildlife migrations, shift by weeks and take a surge of demand with them.
How to find the current answer
Calendar-view fare search across a whole month shows where the troughs actually are for a specific route, which is more reliable than any general rule.
Checking the destination's public and school holiday calendars before fixing dates catches most of the avoidable peaks.
The durable rules are narrower than the seasonal ones: midweek departures, avoiding the day before and after a holiday block, and booking outside the last-minute window.