You need a valid verifiable payment method to make use of the App Store services. Including updating Apps, and downloading free ones.
If your payment method stopped being verifiable for any reason, you need to sort it out and make it so it can be verified.
Once its verified, and you have no outstanding balance, you can then remove the payment method by setting it to "None", and it won't ask for it again.
If you can't choose None when you edit your Apple ID payment information - Apple Support