When you agree to disagree, you're saying that you respect the other person's right to his or her opinion. You're not saying that you agree with that opinion. Take a time out, if you must. If the situation is getting too heated, or you feel that you're not making any progress, remove yourself from it. But don't ignore it indefinitely.
Unresolved issues are usually the most stressful.
Focus on the positive. If you can honestly compliment someone, you'll overcome some of the difficulty of dealing with that person. We all like to hear good things about ourselves. And we all find it hard to be unfriendly or difficult with someone who has said something nice to us. Provide positive feedback to the disgruntled customer - I bet you'll see a change in response.