Interesting.
Found some tips online. Turns out that the priority you set using Task Manager only stays as long as the app is the foreground process. Switching around will reset it back to low priority.
To keep something high priority, you have to force the priority when you start it. The easiest way is to create a batch file using notepad (save it as BTS-high.bat or something). Just use the Start.exe utility to launch the program of your choice in high priority (cmd /c start /High civ4beyondsword.exe).
Wodan