The general answer, is "yes," the employer can deny you vacation time, even after approving it.
You could quit your job, and the employer would have to pay you in cash for all of the unused vacation. But, until you either quit or you are laid off, the employer can refuse to grant you vacation time, unless you have an agreement to the contrary.
If there is an employee handbook in which the rules for vacation time are stated, and the employer violates those rules, then that would be a sufficient agreement, and you could sue the employer for breach of contract. But, you need something in writing to prove that you had the contractual right to vacation time, and that the employer violated your right.
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