I have no problem signing in on my laptop.

But for reasons I do not understand, I cannot get this site to accept my password on my iPhone or my iPad.

Any thoughts?

David

Do you use the Mac Keychain application?

It will attempt to enter passwords for you if you do ... across multiple iDevices it can sometimes lose its way.

If you DO use it:
Sign out of the Café on all devices, delete cookies on all three iDevices, make sure the Magic Café isn't noted in your Keychain application on your desktop computer (it hides in your Utilities Folder - Keychain - highlight iCloud, and scroll down looking for a reference to the Magic Café. If you find one, delete it after making sure you remember your password).

Turn OFF the Keychain on your iPad and iPhone (Settings - iCloud - Keychain - Advanced - OFF)

Note that sometimes folks are using Keychain on their iDevice without knowing they're using it. One telltale that you might be using Keychain is that some internet browsers (especially Safari) will always auto-fill your password and user name for you.
BUT, Keychain and Autofill are two different things that "kind" of overlap purposes - Autofill does just what it's name suggests, and Keychain remembers passwords.

You may think you're just using Autofill, but in fact Keychain has (somehow) been activated in your iCloud account (which is where it lives, and why it can move passwords across all your iDevices).