I found the problem. But don’t know how to fix it.
After looking in the view-source of the page I found that there is a “form-data div” created for every calling of the acf_form function.
<div id="acf-form-data" class="acf-hidden">
.
Once removing all these divs except the first one using the inspection tool in the browser, everything worked perfectly.
The problem is that I don’t know how to define to the acf_form() how NOT to create unwanted extra data-form divs.