When I put on banking mode on my Ipad, I can't open the banking sites.
If you talking about this feature:
Maybe you have to to transfer URLs (if websites are blocked; or certain banking websites are blocked for access?!) by using F-Secure SAS:
with related categories like "Banking Protection related troubles" -> "Site should not be blocked during banking protection session" (after check option ''I want to give more details about this sample and to be notified of the analysis results'');
OR If this just wrongly work under iOS-platform (based on feature's description):
good to contact direct F-Secure Support Channels (chat/phone)^ ;