Hi
What the ideal design process would be:
1. Have a chat with the client to see what kind of people they are and if you think you will get on well with each other. Ask them questions about their business, their clients and what are they hoping to achieve with the site.
2. Sign a contract and get a deposit. Contract should cover you in all possible situations - like in this case what happens if client is not happy with the design, how many rounds of changes, etc.
3. Questionnaire - client need to fill in a questionnaire, this is for you to refer to, when designing the site later on. Questions should be about their target audience, their brand, colour scheme, etc, whatever you need to know to create a successful design.
4. Send them a first draft, to define the direction the design is going in and see if they are happy with that. Best to check from an early stage. Also one draft is enough - in my book t's a mistake to send a few versions for them to choose from. We are looking for quality, not quantity, so I much prefer to spend double the tie on one design, but make it perfect than creating two designs, that don't really fit.
5. Explain your design decisions and ask for a structured feedback. "Lacking a wow factor" is not a valid argument and they should explain why they think the design wouldn't work for their clients and why it wouldn't help them achieve their goals.
If the client is capable of explaining properly their goals and their vision of the website, you should be able to create a design that will work for them.
You need a set number of revisions, otherwise it could end up taking months, doing small changes here and there, or even a complete redesign.
Hope that helps.