I got an answer from the Square Enix Support Centre:

We understand that you have a problem with connecting to our servers as we were doing some maintenance work on them.

However, we think that this issue should be solved by now. If this problem still occurs for you, please do not hesitate to contact us via phone or chat Monday to Friday 09:00 – 18:00.
So hopefully the issue is fixed now and won't happen again. However, I wish they would let us know about these maintenances and the possibility of connection issues in the future.