I think, as with a lot of people who do what we do, I'm very insecure about my mixing. When I finally get a mix to the point where I'm ready to send it the artist, there's a lot of angst involved. I generally don't like anything I do, and I'm sure nobody else will like it either. The adrenaline rush when I hit send on the email with the link to the mix is not all a good one!
Then come the mix notes. By definition any changes anybody wants to a mix means that you didn't do it the way they wanted it, which can easily be classified as a failure. What I've tried to do over the years (and have only lately become even slightly successful at it) is to not take things too personally. It's hard because you've gotten the mix to a point where you think it would ready to go out into the world, but the reality is that it's impossible to hear through other people's ears, and there is no "right" way to mix and there certainly is no such thing as a "perfect" mix.
So, soul searching aside, I think that the feedback can actually help you grow as a mixer (or musician or producer or anything really). What you're always trying to do is to figure out what the artist is going for and make it happen. Sometimes the comments are super specific about sonics (everybody has some mixing experience now) and in a way that makes things easy because you can treat it like a to-do list and just tick things off. What I prefer to do though is try and figure out what the problem they're having is and find my own way to solve it. If they ask me to turn something up I'll usually eq, distort and/or pan it. If they ask me to eq something I'll turn it up or down. That makes me really focus on listening to the changes instead of just doing things because they're on the list.
When you talk about a client not recognizing the perspective I bring, that really points to the heart of what's so difficult about mixing. The first thing I'd say you have to remember is that it isn't your record. Period. Your job is to help them finish their record, so you really need to help them realize their vision, not yours. The other thing is that mixing is a weird job creatively because you have to be able to apply your creativity to an almost infinitely varied pool of music and artists, so you are constantly having to change your creative vision to match the circumstances you are in. One of the ways I try to define mixing is using technology to solve creative problems. The real trick is that the creative problems you're trying to solve aren't even yours, you have to figure out what the creative problems the artist is having and solve those as well as yours.
As far as it informing future mixing, I learn things on every mix! It could be how a rough mix treats something, how I made the chorus explode when there's no help from the arrangement or performance, finally finding a reverb that works on drums, anything really. I'm constantly evolving, dissatisfied and hopefully getting better.