That's total BS. Even if it was abandoned, it was already in a stable state with no significant bugs. It wouldn't just cease to be supported. Your workflow wouldn't have to change. And losing a customer over it? That sounds like complete incompetence on your behalf, which your customer probably figured out. Even assuming that Babel 5 would be abandoned, why move to Babel 6 so quickly instead of waiting a month or so while the nice guides, gulp plugins, etc are made?

Your whole situation and outlook really seems to be blaming anything but yourself for mistakes that you made.