I have heard multiple users report that IOS7 does not remember their passwords, whether for CRM for Phones (Mobile Express) on iPhone or using CRM in Safari on an iPad, and that they have to type in their credentials every time they try to use it.
This is due to a new private browsing feature in IOS7. When private browsing is turned on, no passwords will be stored.
Here is a fantastic YouTube video showing how to disable private browsing. After making this change, I have found that IOS Safari typically will remember your CRM password.