We have had the same problems with sporadic lessons, I think the problem was the change in test in Dec, my DDs instructor was, we think, prioritising those with tests before the changeover. Unfortunately her instructor is her friends dad, which in hindsight was a mistake, as she feels awkward changing but we wanted to get her going in June, before a holiday in July, and DS instructor couldn't accomodate her.
We paid for 20 Lessons in June and she hasn't finished that block according to him, although my records says she has! Ok we have had holidays and he has, but she 2 had lessons from mid October to mid December.
She hasn't taken a test yet, failed her first theory in Nov and is now practising hazards but I think it is catch-22, without regular lessons she is not as motivated to do theory, and I think he isn't prioritising her lessons without her passing theory!
We have had her insured on DS car, and she has driven it a lot, but I am not paying for any more insurance until she is having regular lessons and working regularly on her theory.
We are now at point that if no regular slot (she is at college close to test centre and has a no. of early finishes, so no excuse) or any more cancellations without any immediate replacement, that's it.