Can a company cancel an approved leave on the last minute, even after the employee has paid non-refundable payment for the planned holiday?

If there is a written employment policy which had been provided to you stating they could cancel at any time and would not pay for the costs caused thereby, then they would not have to pay: by you working there and booking a vacation with knowledge of the policy, you could be considered to have agreed to it and so be bound by it.
But without a written policy, notice of which was provided to you, if you booked a vacation in reasonable reliance on their approval of the dates, they have to reimburse you for the costs. They are, unfortunately allowed to cancel the leave for employment (e.g. project, workflow, etc. reasons), since employers have great discretion about scheduling, timing, etc. of vacations--but even with that discretion, they are still held to the consequences of their decision to first approve, then later cancel, the leave. So long as you did not have any reasons to be wary of booking the trip when you did (e.g. they had not warned you that there could be an issue), the fact that you relied reasonably on their approval entitles you to compensation. When person (or business) A acts in a way that causes  B to foreseeably incur costs in reliance on A's actions/statements, A can be held liable for what they did or said. 
Unfortunately, as a practical matter, if they won't voluntarily shoulder their obligation, you'd have to sue them; and suing your own employer can have obvious and significant impacts on your career. If you are planning on seeking other employment in the near future, you may wish to wait until you have a new job before suing (but if not leaving in the next year or two, don't wait--you don't want to run out of time to sue). If/when you do sue, you would sue based on "promissory estoppel":
1) The employer promised you something;
2) They made the promise even though it was reasonable and obvious that you would incur costs based on their promise; 
3) You reasonably relied on their promise (no red flags or warning signs); and
4) you did in fact incur costs based on that reasonable and foreseeable reliance on their promise.
This can held them liable to their promise, or least liable for the costs of breaking it.