Meanwhile things got more crazy because at a certain point the message was that the CNAME was OK, we could request the certificate and then the message returned: Please set up the following CNAME record on your domain name.
As far as I can tell, this is just a DNS caching issue. The client area uses multiple DNS resolvers to check whether the CNAME record is in place, and it’s possible that one of them may have the CNAME record and the other does not.
I checked our logs, and I see that some of the SSL orders you attempted to submit failed because Let’s Encrypt couldn’t complete the DNS verification. This can sometimes be caused by the required TXT records not being setup in time on our end (in the nameservers that the CNAME records points to), or the CNAME record itself not being found.
Given that our CNAME check was also returning inconsistent results, I think the most likely reason is that your nameservers were not consistently returning the CNAME record. But your domain is not using our nameservers, so it’s hard for me to say how reliable or consistent the nameservers of your domain are.