I've played with this some more and found a work-around. The issue seems to be linked to User Account Conrol in Vista. Turning UAC "Off" (with the resulting reboot) allows FSX to update the appropriate Do-27 files. After you're done with flying the Do, you can return to using UAC and the changes to the Do files "stick."
Everything else I tried, such as running with administrator rights, running as administrator, and changing the attributes (from "Read only") of what I thought might be the relevant folders and files had no effect.
If anyone else wants to work at this, or check out the work-around for themselves, a painless way of checking to see if changes to your Do "stick" or not is to simply change something quick like the oil level or better yet, the rudder trim. You'll quickly be able to see it the changes stay in place.