To prevent this sort of thing, we use a technique called "post-selling". Post-selling is a sales technique where you continue to negotiate even after you have agreement from the prospect on something. Basically, you are trying to prevent the prospect from changing his mind later on down the road. The technique works well when trying to get someone not to cancel a meeting.
Here's what it sounds like in your situation. After you have an agreement to meet on Monday at 2:00, say something like this.
You: Great, I'm looking forward to our meeting on Monday at 2:00. One quick question: Should I write this in my calendar in Pencil or in Pen? That is, is there a chance you'll have to cancel the meeting?
Prospect: Well, I have a staff meeting that sometimes runs long, so I might be late.
You: That makes sense. Say, is there a different day or time that would work better for you? I typically need the entire time we've scheduled, so I'd hate to run out of time and not be able to answer all of your questions.
Prospect: Yes, Tuesday is probably a better day come to think of it.
Once the prospect has agreed not to cancel the meeting, they will be much more likely to reschedule other conflicts rather than your appointment.