I am having the same problem. I am running Beyond the Sword v3.13 on two computers in my house using a LAN connection.
I am running XP home edition with SP2 on both machines. I have downloaded all of the updates from Windows on both machines. One machine is a new iMac running XP via Boot Camp. The other one is a regular Windows PC. The Windows PC was running a LAN game with rare OOS errors when connected with a laptop as the 2nd machine. We switched the the new iMac b/c the laptop graphics card is weak, but now we get OOS errors all the time.
Any advice would be much appreciated. If you need other specs info, let me know.
Relatively new at Civ, and loving the game, but this OOS error is really cramping my style. Thanks!