Is it usual that a master’s program refuses to reveal graduation percentage?
The comments above are all correct that this information is available and you have every reason to want it. In reality, it may simply be that the person you are asking does not have ready access to this information, especially if you are contacting a grad director or some kind of advisor. She could manually do the calculation (or, better, should make a habit of compiling it each year so she can answer such questions).  I have directed grad programs and can say that I have access to applications in our online system, so I could tell you how many applied and were admitted, but if I want to know graduation rates, I have to track down each student myself and find out. At the university level, this is probably more straightforward and you can get a rate, but it might not be broken down by program.

So, it may not be fishy. On the other hand, that adviser should know how it is perceived, and should compile the information each year. If it is a university with an entirely online curriculum, it would raise a red flag for me. Especially if it is a for-profit online university. But if it is a major on-campus university with an online offering, it may just be what I described in the first paragraph.