As a freelance designer, you required to be a great designer and have a great relation with your customers.
However, there will be times when you’ll have an angry client or two. So, I’m wondering, have you ever had a client write an angry email to you? If so, were you able to respond to them and make them happy again?
Tell us your story.
Great question @PixelGeek! If you freelance/contract for long enough you’ll probably run across this issue (most likely more than once). In my experience, it’s usually because of my lousy communication or a misunderstanding on agreed objectives. I’ve always managed to salvage the situation by empathically responding to their needs as fast and best I can.
I’m a firm believer that no man is an Island. But if you start burning bridges, that’s exactly how you’ll end up. To win the client back over I always try and speak rather than email. Your tone, expression and urgency can all be lost via email. There are occasions when you have irreconcilable differences, and it would be best for all to part ways. But I have some non-exhaustive quick tips that have helped me make my clients smile again 
I make sure to define with them what a successful outcome looks like. Trying to be as detailed as possible, if you have it written down and agreed upon its harder to go wrong.
If possible under promise and over deliver. Great for when you’ve missed a deadline. I say if possible as this may not be feasible in certain sceanrios. Generally speaking going above and beyond helps bridge disputes.
Regular updates are vital. I also try and assume a client has not read my email if I do not get a response. It helps with staying on top of things and making sure there is nothing missed in conversation. No response triggers a follow-up email.
End all meetings with goals, names and dates. Helping both parties understand expectations going forward.
Just a few thoughts. Would love to hear from anyone else as I still have much to learn on this also.