It is not a conspiracy. It is an industry-wide business model designed to maximize profits. The cookie on your computer tells the airline computer that you are interested in this particular flight. The software on the reservation computer is sophisticated enough to follow your interest even if you change dates seeking a better price
Other factors include the number of people who have looked at that route over the past 24-48 hours, how many times you return to the same flight, and the number of tickets actually sold for that flight. The computer software automatically knows to vary the price it quotes you to maximize airline profits. Even an extra 40 or 50 dollars or Euros on a round trip airfare adds up to a lot of money on the corporate bottom line at the end of the year.
Flushing your cookies is one effective way to counter the software. However, if you are a frequent flyer and use your account on your preferred airline, you are screwed. The account login overrides the cookie placed on your computer. So, flushing the cookie cache does not necessarily work if you are logged into your frequent flyer account.
The tactic to use here is to use another computer or flush all cookies, search and pin down the flight and fare, start the ticketing process, THEN log into your frequent flyer account during the process. By then the airline is committed to offering you the fare it quoted.
Even this is no guarantee. Buying airline fares has become like playing roulette in a casino. The odds vary, but over time and in the end, the house (airline) usually always wins.
I hope this helps.