Firefox 4.0.1 is not secure. http://www.mozilla.org/security/known-vulnerabilities/firefox.html#firefox5

To change your automatic update settings, check here:

orange Firefox button or Tools menu > Options > Advanced > Update "mini-tab"

I've got the updates mini-tab set already so Firefox asks me what I want to do, and it does not do it automatically. I will not change this setting. All I want to know, please, is how to tell Firefox to stop telling me an update is available once I've decided I don't want to download it and install it.

No, as far as I know, you cannot "hide" an unwanted update. Therefore, you may have to just turn off Automatic Updates on the tab noted above (uncheck Firefox).

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If you prefer to experiment, check out the setting described in the following article:

http://kb.mozillazine.org/App.update.promptWaitTime

Maybe if you enter a really huge number of milliseconds you can extend the time between reminders to a week? However, since this affects security patches, you might want to reset it after you finally upgrade to Firefox 5 (or 6, or 7...).