Apple Internet Sharing doesn't stay enabled
I never did find a way of making Internet Sharing stay on, but I did come up with a way of achieving the same result.  With a quick bit of Ruby, I whipped up this solution.

Load IRB by opening terminal and typing irb

Copy and paste this into irb, and hit Enter to activate.

 while(true);sleep 15;puts Time.now.to_s + ": " + `launchctl load -w /System/Library/LaunchDaemons/com.apple.InternetSharing.plist 2&gt;&amp;1`;end


As it stands, the code will re-activate Internet Sharing every 15 seconds. Now, that may seem like too short of a period, but at 15 seconds there's a good chance that the connection will be re-enabled before any connection drops occur.  You can change 15 to any number of seconds that you like.

This will result in a log such as:

Mon Jul 25 09:37:07 -0400 2011: com.apple.InternetSharing: Already loaded
Mon Jul 25 09:37:22 -0400 2011: com.apple.InternetSharing: Already loaded
Mon Jul 25 09:37:37 -0400 2011: com.apple.InternetSharing: Already loaded


It's important to remember that closing the window will terminate the script (Internet Sharing won't re-activate every 15 seconds), so if you need to close the window, consider using screen which is included on Macs.