I think we've all had clients who want to change things constantly, and like other posters have mentioned we call them "thumbprint clients" because the feel a need to leave their "thumbprint" on every iteration.
Sometimes it's easy to feel like these thumbprint clients are "bashing" your design work, as designers we vest a lot of ourselves in our work and it's easy to feel attacked when people want to change our designs constantly, we can feel like they're questioning our expert knowledge.
I've had plenty of clients like this myself, and I've developed a couple of strategies for coping with them. The first, and most proactive is what I've call "come to call establishing expertise." Most of the people who come to us as clients aren't designers, they haven't studied design, they don't know famous designers or design styles and they don't often understand how designers abstract solutions to the problems they give us. When I first meet with a client, I like to really take some time to sit with them, to talk through the design process and also to talk about what they're wanting. I talk about design theory with them, I ask them if they've ever heard Dieter Rams' Principles of Good Design and I explain how some of these principles apply to what they're asking me to design... by the time I begin working, I've established an idea with the client that what I do is more than just drawing pretty pictures and I've instilled in them the trust that I'm an expert at what I do. Establishing Expertise is the first key to neutralising thumbprint clients.
The second thing I do, and maybe even more important than the first, is I charge for EVERYTHING. When I first started in the creative industry I had a boss who told me the key to life was "line items", the more line items you can add to your invoice the more the client understands the value of what you're doing. At the time I didn't understand, I felt bad charging the client for something I thought had been our fault, but over time I learnt that if you don't show clients the value of your time then they will take it for granted, not because they're bad people but simply because they don't understand. Now when I design anything, I provide a proof at the end of every design iteration and I charge my clients for it, even if it's a nominal fee like $5 for sending them a PDF I make sure it appears as a separate line item. When my clients make revisions to my designs, I enter these revisions as a separate line item with the date they were requested. I once had a client I charged over 20 hours of revisions to on a very basic brochure design and after that job, they never asked me to perform as many revisions.
Above all, remember that if someone employs you, and they keep coming back to you, then they must like your work. If they don't like what you do, they'll stop coming back and that's a good thing, it frees you up to work with people who do like what you do. Make sure you approach every client with confidence and charge them for all the work you do for them.