Hi,
I was able to dig into this a bit deeper. Actually I could figure, the following.
The Joomla! default code, which I use to create the date field, adds a class="hasTooltip" to the input of the date field. This is fine as long as the (mootools) core.js is not included in the page. If the core.js is included it will treat the input element as if it were a tooltip, which means, it adds a style="display:none" to the field on focus out. This is what happens on your website and with your custom css you just enforce, that the element is displayed anyway.
By the way, you could make the css more specific, so that it does effect less other elements.
.visform input.hasTooltip {
display: inline !important;
}
Joomla! is on it's way to change the default javascript library which is used with Joomla! from mootools to jQuery. So usually you have only jQuery included in the website and jQuery has another way to display tooltips, which do not effect elements with .hasTooltip class attributes. But there are still some Joomla! core compontents (like the com_tags) which do include the core.js
So actually I think, this is sort of incompatibility in the Joomla! core code itself. (Maybe they changed the date HTML som Joomla! Update). So you could either think of opening an issue on the Joomla! bug tracker or just hope, that the problem will vanish, when Joomla! has finished the switch to jQuery completely and stick with your solution until then. (And obviously it is possible that a template includes the core.js as well, as long as it is part of the Joomla! Framework).
Kind Regards,
Aicha