Impossible to transfer mobile banking app data between factory resets
Assuming that the IT department of the bank has implemented some sort of check in their Android app to ensure that you can't restore its data between different installations (which also includes factory resets), they're probably using something along the lines of a unique ID such as ANDROID_ID.

This answer (and specifically Seva Alekseyev's comment) explains what I suspect is causing your issues; this ID also changes on factory resets. This is purely a security measure and a very good one, because it would be terrible if I could log into your Google Play account on my phone and restore your banking app's data from the cloud, allowing me to access your bank account, right?