I have this very weird behaviour with Firefox TextArea.
I was having the HTML like this:
document.getElementById("txtStatus").innerHTML += "SomeResult"
Well, it works perfectly until you change the content of the TextArea manually, subsequent click on the button will "change" the innerHTML property but the display won't refresh and show you the changes.
I don't know what went wrong, but I got it kind of solved by using .value instead of .innerHTML, which it might be due to the design of innerHTML rather than specifically to TextArea.