I have to agree with JulieP, ongoing characters need to be interesting and realistically flawed. I feel it is also important that the character appear to grow over the course of time. There are many series where the character is the same in book 15 as in book 1. There doesn't appear to be any personal growth or knowledge gained from past encounters. Even if a series isn't taking place in real-time, it is presumed that events are taking place over a few days, weeks, months, or years. As a reader, I expect to see the lead character grow rather than remain static. Flaws make us human, but an inability to change comes across as arrogance coupled with ignorance whether it's in a person or a character.