I've had Doom 3 a while and haven't run into this problem, though you might want to try clearing your 360's cache and see if that helps at all.

Go to the system blade on the dashboard and then select memory, Press Y on the Hard Drive symbol and then press X,X,Left Bumper, Right Bumper, X,X. Once you do this a message will appear saying: Do you want to perform maintenance on your Xbox 360 storage devices?

Do so, and see if that helps at all.