I just tested it and it also works. The only way i could reproduce this issue is when you are in the ‘Contact Us’ page and click in the ‘Contact Us’ link in the top. That happens because when you click in the ‘Contact Us’ link (while in the contact us page) the theme loads the content of the page using javascript.
That works great for static content like the text and images that you have in the page but unfortunately loading a page using javascript doesn’t automatically load the dynamic content (like the form in this example) it needs to be loaded manually. That is why it works fine on refresh (because refreshing a page will load the content the normal way which will also load all dynamic content).
Unfortunately there is no way to fix this in the smart forms plugin since the problem really is that the theme is loading the content using javascript and not the standard way. To fix this either the theme needs to be modified to also loads the dynamic content using javascript or it needs to load the content of the page using the standard way and not javascript (generally the themes that load content using javascript also have an option to disable this feature).
Regards!