Try this.
Download an app (paid or free doesnt matter)
Enter your password - app installs.
Now within 15 minutes go back and download another app (again paid or free)
App installs.
The issue is that iOS caches your password for around (possibly exactly) 15 minutes.
The reason I heard for this is that its to save you time when you are setting up your phone for the first time installing loads of apps...
Just do what I do, when your card expires dont update your details with itunes if I want to buy something I have to go and buy an iTunes voucher... yeah its a pain in the arse and it takes longer but at least I know that the most my kids can spend when they are playing with the phone is the £10 of pre-paid credit that i put on it... no nast surprises when mr visa sends a bill!