The error indicates that the validation could not be performed. This could have several causes: the VIES service could be unreachable, overloaded, or block the requests. In some cases, the server itself could be blocking the call to that service. The fact that the VIES page works is not necessarily relevant, as that page runs the check internally.
The following post explains this in more detail: https://www.ads-software.com/support/topic/faq-vat-is-not-deducted-when-entering-a-valid-vat-number/
Here you can also find the instructions to enable the debug mode and review the log, which should contain the details of errors encountered during the validation: https://www.ads-software.com/support/topic/faq-how-to-enable-and-view-the-vies-validation-log/. With that information, it should be easier to figure out why the VAT number could not be validated, and find out how to fix that issue.
Note: we would suggest to first enable the debug mode without entering your own VAT number in the settings. That will prevent any unexpected error from interfering with the save operation for the debug option.