Hi,
In the file checkout / show_block_fields, which you can edit via the menu Display>Views, you have the line:
window.Oby.registerAjax(['checkout.fields.updated','cart.updated','checkout.shipping.changed','checkout.payment.changed'], function(params){
If you change it to:
window.Oby.registerAjax(['checkout.fields.updated','cart.updated','checkout.shipping.changed'], function(params){
then the fields area won't be refreshed when you change the payment method and thus the fields won't be cleared.
This, however, means if you configured the fields to display for only some payment methods and not others, the fields won't appear/disappear when the payment method is changed.
Another approach would be to configure your checkout in several steps, and move the payment and fields views onto different steps. That way, the problem would not happen.