A fare quoted in the morning can differ by the afternoon on the same flight. The movement is produced by how airline inventory is structured rather than by any reaction to an individual searcher.
Seats are sold from separate fare buckets
An aircraft cabin is divided into fare classes, each holding a limited number of seats at a set price, with restrictive conditions on the cheapest.
Bookings fill the lowest bucket first. Once it empties, the system quotes the next one up, and the visible price steps rather than drifts.
So a fare increase between two searches usually means somebody else booked, not that the airline reacted to your interest.
Buckets are managed against a forecast
Revenue management systems predict how many seats will sell at each price and adjust the allocation as the departure approaches.
If a flight is booking ahead of forecast, cheap buckets are closed early to preserve seats for higher fares later.
If it is booking behind, cheaper buckets can be reopened, which is why fares occasionally fall after rising.
Business travellers explain the late increase
Fares typically climb steeply in the final weeks before departure because that is when time-sensitive travellers book and they are less price-sensitive.
Holding seats back for that period is more profitable than selling the whole aircraft cheaply months in advance.
The pattern is strongest on routes and days that serve business travel, and much weaker on leisure routes where late demand is thin.
Displayed prices depend on the channel
Different booking sites hold different agreements and access different fare inventory, so the same flight legitimately shows different prices.
Currency, point of sale and applicable taxes add further variation that has nothing to do with the seat itself.
Comparing across a small number of sources catches most of this, while checking many more tends to add effort without adding information.
What repeat searching does and does not do
The belief that searching repeatedly raises the price is widespread, and airline systems generally price on inventory rather than on an individual's search history.
Sessions can retain a previous quote through caching, which produces the appearance of a personalised increase without one occurring.
Checking in a fresh session is a reasonable way to rule that out, and it is more useful than clearing data in the hope of finding a hidden lower fare.