Hi Steve,
thanks for the additional information.
Are you testing on a desctop pc or on a mobile device?
This sounds to me like a very special sort of caching problem. I say special, because I cannot remember that I have heard of this similar behaviour before and Visforms is used by thousands of people. And I say special, too, because, if you publish the form via menu, the standard Joomla! cache does not cache the page, so it is most probably not the Joomla! cache that bothers you, but some other cache.
Basically, if the page is loaded from a cache (no matter where the cached page comes from) this would look excatly as you describe it, because the second time you submit the form, Visforms "thinks" the form is invalide (there is a mechanism that prevents a user from submitting the same form instance twice, that is not triggered properly if the page is loaded from a cache) and will redisplay the form. Usually there would be an error message ("you can send the form only once") and the user inputs, which you have already made would be inserted into the form, but because the page is again loaded from the cache (which holds the page with the empty form) you just see the empty form again and no error message.
Sadly I cannot tell you, why or where the page is cached (is this due to php settings of your local test system, is this due to .htaccess settings.....??.)
If you like too, you can provide my with an Akeeba Backup backup of the website and I can look, whether I can reproduce the problem on my local test system (send me a link, where I can download the backup to contact@vi-solutions.de, then). If I can't reproduce the problem, we would know, that it has something to do with the settings on your system, if I can, I would gladly debug this.
Regards,
Aicha