Five times in a row in three weeks is over the top, unless she's got some special circumstances going on (which doesn't seem to be the case if she's there at other times). I'd be livid. You say she talks to you like a friend -- it sounds to me like she views her lessons as favors to friends and not something that's part of her job. For comparison's sake, if I'd called my boss five minutes before I was supposed to be at work for the past five days and said I wasn't going to make it in, he'd certainly be initiating a serious conversation.
I would put some thought into other times that you can do lessons, in case your coach responds that the timing is the issue, although that's still not a good excuse. I'd also write down all the times recently when she cancelled on you. Then, the next time she begins chatting with you, chat politely and then say, "Hey, you've canceled our lessons five times in a row. We haven't had a lesson in a few weeks. What's going on?" Or, if she comes up to you and asks about a lesson, remind her that she's already canceled several times.
If her response doesn't make you feel better, or if she keeps canceling, I think you should talk to your parents again about finding another coach. It's your money and you've got a valid argument.