Many factors. We all take our chances.

If you are REAL SMART, and have access to a new instrument or data archive, or are a truly brilliant theorist, you have a tremendous shot at stability because you are a highly-prized researcher. If you are an average astronomer, it really depends on whether you have achieved some type of notoriety in research, and these interests match those of the institution with a position opening at the exact time you need a job. Timing is everything in science. You have to be 'on the market' at the same time as there is an opening for your dream position, and once hired, you have to get tenure by showing your ability to attract research money to your new department and to be regarded as a prolific and talented research scientist. Because there are twice as many new Phds in astronomy as there are stable jobs, institutions can pick and choose exactly what they want to hire almost down to the shoe size. You have to stand head and shoulders above every one else via your research, discoveries and your list of references to get a job.

Stability is now an illusory goal for many of us. We just want to stay in the profession for one or two more years and consider ourselves lucky. By the time you are in your mid 40s however, it starts to become quite a drag living one to a few years at a time. You never think of BIG projects or long term research goals because you have to produce lots of papers every year to keep your bibliography growing at a reasonable rate. Institutions have also learned that it is cheaper to hire 5 post-docs than offer one of them Tenure, so like every other professional career, the Employer has the upper hand and insures that a cheap labor force is created and maintained to pump out more research papers and attract more grant money.

Welcome to the real world!