Players are transfer listed constantly but you are only able to see a part of the whole transfer list every time you log into the game.
With each re-log you get to see a different part of transfer list. This is done in order to prevent cheating and to prevent swapping players between fake teams. If you wish to save a player you liked on the TL, either place a bid for him or add him to your favorites. Placing a bid will automatically put that player in your favorites list, allowing you to see him in the next log in.