Hi,
The error messages are displayed in the template, but in this case there was no message. Nothing happened at all.
Anyway, the problem seems to be solved.
I noticed that the URL of the button 'Proceed to checkout' in the cart module varies a bit, depending on the page on which the cart module appears.
In my website the cart module is assigned to the main Hikashop menu, and also to a hidden hikashop menu showing a product listing (used by the filter module), the User Control Panel menu, and 2 Joomla menus showing articles (customer information). So there are 5 slightly different ways to enter the checkout.
I have redirected all links to the URL of the main Hikashop menu (via sh404sef).
And since I've done that the customer complained no more and orders came as usual.
Hurray!
Thanks,
Udo