During the first 24h game day the used market is refreshed every 3-4 hours or so. Meaning that you do not have to join at the first minute.
But the fact is that during the start up phase planes are grabbed quickly from the market, and it should be like that too - to some extent. As you can't except to have just the right A320 with right engines available 24/7 when you happen to need it. The market is refreshed several times a week but not every day though. That's not intentional feature to add difficulty but just a chance in general level to all games based on experiences from past games.
The number of available used planes has been increased and the ratio between models is also introduced to this version. Meaning more A320 & B737 and less IL-62 and similar .. Was posted to "AWS 1.1 updates" thread some weeks ago. Other updates too, check that one.
And there's also the 3 minute grace period, so if you can get to the buy/lease menu the plane is reserved for you...
btw. there is 401 used planes on the market at the moment (!) ... should be enough to choose from