You get an alert about resending POST data if you go back to a page that was previously requested from the server by submitting form data via a POST form.
Firefox can only make sure to get the same page by resending that POST form.
Firefox doesn't know what that form data means, so Firefox asks for confirmation before resending that form data as such an action can cause you to repeat an action and buy another item or post a message another time.
A way to prevent that pop-up is not to use the Back button, but to open links from a page that was requested from a server by sending a POST form in a new tab (window) with a middle-click or a Cmd + left-click.
Then you can close that tab or window to go back.

That isn't the kind of thing that is happening. I haven't used the back button once. I have only clicked through to the page I was on and the add-on I have wants to refresh the page but it isn't working properly.

The same happens if you refresh a page that was retrieved from the server by sending POST data. Such a refresh will cause the same pop-up message to appear. You can't refresh such a page without confirming the resend.

Just "don't use the back button"? How about using IE, that's what I've done. Using ctrl+left click does nothing on my system (Win7 & FF 3.6). Problem remains. Will FF4 solve this problem? Meanwhile, I've gone back to IE, which also works with Blackboard Vista, while FF 3.6 does not.

I use intellicast.com a lot to look at local radar data. I have to refresh the page to look at more recent data. This popup is a 'do you really want to do this' and is a major PITA. I understand the reason behind it .... to prevent someone from making a 'second request' and making a request that they really didn't want. Well, I'm sorry. Protecting the idiots is not a function of a browser. It isn't the responsibility of Firefox to prevent someone from doing something stupid. It's the responsibility of the dude pounding the keyboard. The 'resend' popup might be a good idea but is a poor execution.

I went to Tools-Options-Advanced-Network-and cleared the offline storage. It's working now. Don't know for how long, though.

Regarding the Firefox prompt, "To display this page, Firefox must send information that will repeat any action (such as a search or order confirmation) that was performed earlier." Recently, I noticed that if I ignore the "Confirm" box for this prompt - just "x" out of it, and then do a back arrow, it goes back to the page anyway (without having to click resend). This demonstrates to me that Firefox doesn't even need to resend the information - it's just a glitch.

I found that when the "accept 3rd party cookies" is disabled the same problem exists. Turned it back on and set "Keep until", to "I Close Firefox". Resolved my problem. Hope this helps