One should never assume that it's impossible to slow down, or that by doing so, someone is going to shame you for it. Learning to stay focused isn't going to lead you to less work, but it will certainly help you to manage stress, allow you to do more, and generally provide a smoother working experience.
You have a long relationship with this customer and it is exactly at this time they need to know that you're genuinely upset with whatever has developed. You need to take a breath before you engage with customer or staff. You also need to understand that giving up completely to whatever demands are made and make the situation go away is not always necessary.