I'm running the latest version of Limwire. Since I updated, each time I reboot my computer, I find that the 'Stop Sharing File' facility in the Library has deactivated. Although I stop the file share, next time I reboot, all those files are being shared again. Is it just a bug?

Try this: Delete LW's preferences folder when LW's properly closed. See point 3 here & also point 2 if you've used older versions of LW in the past (there could be a folder in either location).
Fixes for LimeWire
This will kill all of your settings within options, you'll have to go back through afterwards & reset things. If you're not sure of your settings, go through LW's tools > options & write them all down, so that you can reset things later.

Are you using a stable release, or a Beta version of LW? If you're using the latest Beta (4.13.12), you could post over here at the Beta forum. You'll have to register there before you can post
Bugs and Beta Testing - LimeWire Forums