Internet Sharing failing on Mac OS X Lion Server
The answer is yes.

I'm typing you this answer through an InternetSharing
connexion provided by an iMac running MacOS Lion (10.7.3) where no one is connected:

me -&gt; MBP    ………Wi-Fi………   iMac   ………Ethernet………   Internet 
      10.6.8               10.7.3


I'm using such a connection for professionnal use
since MacOS 10.4 with no one connected (on the Mac running InternetSharing). This connection was used by 5 other Mac (10.4, 10.5,
10.6) and might be considered as a nearly professional grade network.

When you login when your InternetSharing is faulty, could you type
in a Terminal or xterm window:

ifconfig -a
ps ax | egrep '(bootp|natp)'


My first blind guess is that your main Ethernet connection was shut down
under the responsability of your Energy Saver tuning.