Hello. If the error does not occur when you are logged in, the issue is most likely related to caching. Your logged in administrator visit would not normally be cached, but public website visits would be. That would explain the difference.
We recommend excluding any page with a form on it from caching. This plugin can do that for you automatically in most cases:
Here is another method if that plugin does not work for you:
If you have any other questions, please let us know.