Buying into a co-op is a decision with long-term repercussions. Co-op boards don't simply want to believe in you this year or next year, but for the next 20 years or more that they hope a buyer will live in the building. The best way these boards have to predict the future is to look at the past. How stable have you been?
This may make it a bit more difficult for the screenwriter with one big score, the man or woman on a fourth spouse, or someone who's had six jobs in eight years.
That said, most stability issues will be reflected in the specs of your application package. Making it to the interview stage implies that the board's willing to overlook your footloose past -- and you can and should sculpt responses explaining why your salary has fluctuated between $20,000 and $400,000 over the past 10 years, and why, despite this, you're now on a perfectly even keel through at least the next century.