FWIW considering our current low earth orbit capabilities, which are not existent I see a trend during this down time to focus more on the science sorta background people than Aviators. That is not to say they won't focus back on aviators once the Orion Program is up and running.
I worked as a Security Police Officer at the "Cape" for a year before my current job. I know two Astronauts pretty well and keep in regular contact with them and have interacted with several. The guys operating the orbiters from the front were most always USN/USMC/USAF Aviators or NFOs then a mix of mission specialist from different places. Each of the Astronauts qualified with the T-38 talon and solo'd each one regularly regardless of who they were. There are mixed reasons for justifying this but for whatever reason I can't tell you which of the 9 stories I heard was the official reason from Nasa.
From what I've gathered talking to NASA employees and consultants, aviation experience is a good way of ensuring that people who go to space can handle the complexity of the job. Pilots well versed in high-speed/complex aircraft develop decision making skills in a complex and constantly changing environment while interfacing with a machine and dealing with time and physiological constraints, all while being able to remember and apply relevant information from volumes of knowledge. A person who can do all that will better understand their responsibilities of space flight, and more level-headed in an emergency, than a non-aviator.
This is purely my own speculation: I think they will always want at least one career military aviator per vessel, because the aforementioned skills will likely be more developed in him than they will in the other astronauts.
The professor of mine (consultant) went on to say that becoming an astronaut is not as simple as getting your degree and the few years of relevant experience. That's for the guys who get their STEM degrees, fly in the military, and become test pilots towards the end (flying is not a STEM job). They're really looking for people with a solid decade long work history with recommendations at all levels, various awards, and a plethora of projects to their names.
Look at any astronaut bio, these guys are mostly high-speed types who blast through education and have experience in tons of different fields before getting picked up.
http://www.jsc.nasa.gov/Bios/astrobio.html
