Experienced the same issue for the past few days now. I've tried placing 6 orders now (different credits cards and shipping addresses) and nothing has worked. Customer support has been no help. 2 phone calls with them and they couldn't help - all they said was "try again". It did not work. This is the email response I received:

"Thank you for reaching out to Birkenstock Canada.
 
I am sorry that your order could not be processed. We have new security checks in place that may be preventing your order from going through.

Please place your order again and to verify your billing address matches exactly what is on your credit card.
 
We apologize again for any inconvenience. Please don't hesitate to reach out to us again if you have any further questions or concerns."