Say you once had a very promising writer, a writer you thought would go places one day. You got on very well with the author; you were friends. ( I never mistake representation for friendship) You sold that writer's first books to a major publisher for big advances. However, the books did not sell as well as everyone hoped, and the writer had a hard time getting said publisher to accept fourth novel, also because she would not accept your wise advice. The writer went into a funk and wrote you a rather rude and ungrateful letter, firing you.
After a year, the writer writes back, saying she has a red face, a sincere apology, and a peace offering. She admits you were right all along, and tries to explain her reaction at the time. She has written a great new novel, a highly commercial one, and that is her peace offering. She tells you that you are the most wonderful agent in the world, that you are her first (and only) choice for this new novel, and she asks for a second chance.
Would you give her that second chance? Would you forgive?
You know what happens when the next problem arises? The same thing. People hardly ever change. They want to think they have, but they don't.
I get enough crap from the amateurs in the slush pile. I don't need clients who act like spoiled brats. Someone else can take them on.
It's one thing to not take advice and fire an agent. That happens left and "write". The trick is to not do it with a "rude and ungrateful letter".
I've fired clients, I've been fired. It's never fun but it happens. I've never regretted not taking anyone back, no matter how well they sold later, if they were snots in their dealings with me.
No matter what, no matter what, keep your conduct businesslike. No matter the provocation, not matter how well justified you may feel.
And, when you end up looking for another agent, I also don't say "she was a snot" to anyone who asks. All agents know people part ways for a variety of reasons. I'm not going to poison your future relationships for spite. I might want to..but I'll vent on the blog instead of to your new agent over drinks.
On the other hand, Miss Snark is an unforgiving cold hearted bitch. It certainly won't hurt you to write to your agent and say "you were right, I was wrong, let's go make some more money together" but don't be surprised, and don't be offended if she writes back "not quite right for my list".