What determines which crew missions are available?

It's a random assortment based on your skill level. Every mission has a minimum skill before it becomes availiable, and there is a maximum number of availiable missions at each tier, which is based on your skill and increases with it.

You can refresh the list by zoning into a new area, or logging out and back in.

Firstly, you could be seeing a bug that's hiding your missions, from the Crew Skills FAQ on the official forums:

12. Help! I can't see any of my Crew Skill missions or companions! What do I do?!

This is a bug with the UI (user interface). If you are experiencing this problem, all you have to do is hit [CTRL+U] twice to reset your UI. Hitting it once will turn it off, hitting it again will turn it back on.

Secondly, they come from a random assignment of missions that changes as you run missions (if you can't see any you want at the moment just run a couple of Companion Gift missions to force them to refresh).

And lastly, at higher levels you also want to be checking the GTN for single-use crew missions. You're given less missions at the higher levels and expected to buy some of them from other players. Traded missions often give well above average results, but also have a chance of failing absolutely, so they are a risk but often pay off.