My manicurist did this exact thing to me. We had become quite good friends, she'd even offered to look after my cat when I was away. Years of custom with no lateness/missed appointments etc. Then on ONE occasion I ended up coming out of a docs appointment later than I'd anticipated, had given her a heads up with a message, full apologies etc. It wasn't xmas, she wasn't busy - nobody in the shop when I arrived and nobody arrived during my appointment or as I was leaving.
Like you I apologised profusely, explained the situation, told her to cut the appointment short if needed etc. Got daggers, silent treatment throughout the entire appointment and charged extra at the end.
I'm self employed and work on appointments, I get how annoying it can be. I'm mobile and drive to my clients, and sometimes they're not home so I'm sat around waiting for them to arrive.
But I still understand things happen sometimes, we're all just human trying to spin a million plates at once. If a customer is usually great and this is obviously a one-off I'd be understanding. I would never treat a good paying reliable customer in that way because of a one-off lateness by a few minutes.
I never went back. Found someone else. She lost reliable frequent loyal custom of several years because of that ONE instance.