I have exacly the same problem today. Trying to update an expired credit card for Creative Cloud - 'My Payment Information' link shows for 5 seconds and then disappears.
I follow a link from the email that adobe sent me which seems like a differen route to get to payment details - for some reason it is in the North America store and I don't have any control over that. Anyway after ticking the t&c box, I get thrown an error message.
I'm using chrome on an iMac - but it doesn't look like the browser is the issue.
Am I to understand that the way forward is to open a new CC account with a different email? That sounds like it will cause all sorts of problems.
Is there a better solution - can I ring someone and give new card details? Its all a bit messy.
Thanks