I have an iPod touch. The Facebook application was working fine until three days ago. When I start the Facebook app, it shuts down immediately. I tried restarting the phone but it's the same. I tried deleting the app and reinstalling, but it will not allow me to reinstall stating the app requires iOS 4.3. How can I make this work? Why would it have all of a sudden stopped working?
Did you sync your iPod Touch with iTunes recently? An iOS device won't download newer versions of an app if they can no longer run on your current iOS version, but iTunes doesn't stick to that rule. So if the Facebook app was updated in iTunes, and then you synced with your iPod Touch, it may have been updated to a version that it can't run, hence the immediate quitting.
You can verify this by going to Settings → General → Usage and tap on the app under the storage setting. You'll see a version number, and you can Google that to see if you have a version that supports old iOS or not.