There are minimums for positional players and pitchers. You must maintain 12 positional players and 6 pitchers on your active roster at all times. If sending a certain player down will put you below that limit, they will not show up on the list.
Another reason that players may not show up is that for leagues that started on Dec. 12th, 2007 or after, leagues will have a salary cap of 10% of the league salary cap for the minor leagues. This was done to help combat a strategy where high quality, low IP/PA players would be left in the minors while playing low quality, high IP/PA players in an attempt to save those good players for only when they needed them.
All open leagues and theme leagues where the commissioner chooses to have this salary cap, will have it imposed.
When you are looking to bring up a AAA player, if there is a minor league salary cap, only those players that don't put you over that cap will be on the list.
Ex. You have 8 players in the AAA in an $80 million cap league. If the salaries of those players is $4,000,000 and you look to call up a $200k player, you will only be able to bring up players that cost less than $4.2 million ($8 is the minor league salary cap, $4.2 million is the $8 million salary cap - $3.8million as the cost of all of the remaining players in AAA).