As a travel agent, I would like to make a couple of corrections to statements made in several of the posts above -
1) For tickets issued by travel agents, nearly all of those tickets can be changed directly on the airline website and do not need to be handled by the travel agent. This is true at any time, not just T-24.
2) Very few airline tickets these days involve a commission paid to the travel agent by the airline. Airline commissions for travel agents began to be eliminated more about 20 years ago and now are almost non-existent.
3) The only airline tickets that specifically need to be handled by the issuing travel agent are those that involve special agreements offered by the airline either to a corporation who purchased the ticket through the travel agent or to the travel agency issuing the ticket. These tickets have a special code that specify the terms of the ticket and many of the "regular" airline phone agents are not familiar with such agreements.