There was a time when I madeamistake because of miscommunication between [my customer and me / me and my customer / my customer and I /I and my customer].
"i once made a mistake because of a miscommunication between a customer and me."
You could use "misunderstanding" instead of "miscommunication," but the former could be something simple: Your customer said "size ten" and you hear "size nine," so you brought the wrong size shoes. But "miscommunication" allows for the possibility of a discussion in which each exchange mystifies both parti