It could be any number of reasons. The following things I throw out may or may not be potential factors as I am unfamiliar with the home, location, local economy and demographics, but they can affect numerous scenarios.
As you stated, there are not too many house in the area like yours, which is typically a good thing to be able to set yourself apart. My guess would be with a 5 bed/3.5 bath, the renter pool looking for that size of structure is significantly smaller than a 3 bed/1 or 2 bath, leading to potentially higher vacancy rates. The same size of family that would fit in your home might try to make a 3 or 4 bed house work by doubling up children in bedrooms and they might be fine with a 2 bath home as opposed to 3.5.
It could also be affected by location. How are education and employment opportunities here versus 30 minutes away. You may be competing not only against similar houses in the area but surrounding communities.
What is your demographic makeup? I personally live in an area that is going to see the number of senior citizens increase 97% by 2035, so a home like this in my area may not have the same demand as a 2 bed/1 bath home for someone who has grown children, is approaching retirement and looking to downsize to something more manageable.
Lastly, it could be price. From the link you provided it appears that as early as this time last year it was advertised at $1,750/month. Maybe that was under market rent, maybe not, but like many things in life it is only worth what somebody is willing to pay for it.
Again, I'm not saying any one of these things is the reason behind your vacancy. It could be none of them and maybe you just need a few more outlets to market through in order to reach your potential tenant.
You have a beautiful property and I hope you find yourself a great tenant soon!