For your Bank Check your cookie policy in Privacy settings or in about:config network.cookie.lifetimePolicy = 2
cookies are deleted at the end of the session 0 = Accept cookies normally 1 = Prompt for each cookie 2 = Accept for current session only 3 = Accept for N days concerning Abrowser you could try a https://support.mozilla.org/en-US/kb/refresh-firefox-reset-add-ons-and-settings & Hidden file .mozzila https://support.mozilla.org/en-US/kb/profiles-where-firefox-stores-user-data
