Usually sites only working with, or only wokring properly with, IE is because of the way the webpage has been coded (laziness if you ask me! )
Unless they have had an upgrade since it worked for you, and it not working, the tech support lady is wrong (but is probably being told she isnt) becuase if nothings changed, it never would have worked to begin with.
Unless you upgraded your firefox in the past week like I did, and still only if it has never worked with the new version. If it worked once, it should always work, and if it doesn the bank has changed something.