Aline,
I see your issue with this customer as a communications issue. Why, because it was an email conversation. Personally, I encourage my customers, suppliers, and team members to communicate in any way that is efficient and accurate, but we follow the following order of importance:
Face to face - phone call - email - Post Office Mail - fax - text - video/audio chat - smoke signals! Seriously, I do add the line about smoke signals as a joke, but when it comes to that either us, or the customer are already in trouble, or both!
What I'm trying to say is that email is a great communication tool, BUT with email you can not:
Understand the tone of either party.
Understand the inflection.
Confirm receipt, and return transmission.
Control the delivery, landing, and understanding of the communication.
I've seen more business deals go sour because of poor email management. Once this customer replied to your email, I would have taken it up a notch and picked up the phone, or payed them a visit. Sure this takes more time, but the CUSTOMER SERVICE you are providing is better than shooting emails back and forth that are getting either party no where. Either way, you will probably thank the customer for calling on you, but by improving the communication, the referral they give to their friends and families may be better than the referral you will receive with an awkward email communication.
This post is a perfect example, I'm having a hard time conveying what I'm trying to say, but if we were here talking, or on the phone it would be more coherent.
I like what your SBA coach said, "Why would you want a customer like this..."?
Good luck, and let us know what happens!