OK. What about any 3rd party “privacy” or “cleaning” software (CCleaner, for example)?
And the issue does not occur with your other browsers?
Does the problem occur if you create a new profile and try it in that profile? (Make sure your original profile does not have any open windows; only the new profile should be open.)
In other words:
- use the new profile to fully log into the bank site
- do not log into the site again with any other browsers or profiles
- next time you log into the site use the same new profile