I had major issues until I tried this:
Remove all leading zeroes in the account number. Maybe that was fluke but worth trying.
My account number on the physical card is 8 numbers long, with one leading 0. However, the account number on the pdf card sent from alitalia is 10 numbers with 3 leading zeroes and in the beginning I only could log in with this. Now, the website says "wrong format" when giving 10 numbers long, so I tried 8 numbers long, on many browsers and for a long time. No dice.
Just before giving up, I tried to skip all leading zeroes and wham! Success!