This came up as a detail in a discussion of potential size limits of advanced civilizations.
It’s actually easy to keep goals constant for any fixed time horizon, such as the time until the heat death of the universe. Implement the goal homeostat as a program plus a robot along the same lines as DNA plus a cell. The program specifies the robot and the robot checks the program to make sure it hasn’t bit-rotted. With error correcting codes, the check can be made arbitrarily reliable without needing many extra bits.
(If you doubt this, I can prove you wrong in only 10,000,000,000 years! So there!)
Original version, March 2011.
Updated and added here June 2011.