As Burn-it says "The session cannot tell whether you are typing a reply or have left your machine!".
So if the bank's timeout is set to, say, 10 minutes and it takes you more than 10 minutes to type your reply, then the timeout will likely kick-in.
Right-click the tab in your browser and select "Duplicate" or its equivalent (depending on your browser. You should then have two tabs sitting at the same point in the site.
Start typing in one of the tabs and every few minutes flip to the other tab and move around the site in some way. Then flip back to the tab where you were typing and continue typing. Do the flip back and forth (and move around the site) as many times as necessary to allow you to complete your typing.
Another alternative is to compose your wording in another application (e.g. Notepad) before logging in to the bank site and then copy / paste the wording in to the bank's site (if it will allow).