Hide out-of-stock item options on website

[beefolks1]

I am looking to remove out-of-stock item options from the website.

As an example, I sell honey.

Honey has two option features - size and varietal.

For this example, I have four options (sizes) of Buckwheat Honey.   I am out of 5-gallon buckets of Buckwheat Honey (stock = 0).  I also have it set where that particular size is not enabled on my office site. Since the website draws products from the office database, you'd think this would be good enough to hide it on the website.  However, it still appears on the website, despite not being available in the database the website is pulling ino from.  (Hope that all makes sense?)

I have the toggle set such that a zero inventory SHOULD be removing the option/item from the website.  But it is still there.

Help?