Christen, did you enter the limit in "WooCommerce -> Settings -> Inventory", on the field labeled, "Maximum Quantity Limit Per Product"?
My tests show that this works even if you disable the "Manage Stock" check-box on the Inventory settings page.
Gyuen, my tests show that it works on the product page.
You could try disabling all plugins (except for WooCommerce and this one), then test it to see if it works. If problem persists with all plugins disabled, then it may be a compatibility issue with your theme (test with Twenty Fourteen theme to see that this works). If the problem is gone, then enable your plugins, one by one, until you catch the conflicting plugin. I hope this helps.