Thanks for the tip, Andrew. Turns out that "saving" a DNG from within ACR does embed the custom profile. However, just clicking "Done" in ACR to update the DNG does not. At least on my system it does not (CS6, ACR 7.1). Strange, to say the least.
I could swear that clicking "Done" used to work several versions ago. Maybe I'm having a senior moment, but I suspect a bug.
1. In ACR, assign a custom profile to a DNG file, click "Done", close Bridge/Photoshop.
2. Remove the custom profile file (*.dcp) from profile directory.
3. Re-launch Bridge (which forces a rebuild of the profile list).
4. Open the DNG file in ACR and observe that the custom profile is not there anymore, replaced by Adobe Standard.
5. Cancel ACR and close everything again.
6. Move the profile file back where it belongs.
7. Re-launch and reopen the file. Voila, the custom profile is back.
So it looks like just clicking "Done" puts the custom profile name in the DNG file, but not the profile itself. When ACR opens the file it looks for the profile matching the embedded name. If it can't find it, no warning or error message, just a return to whatever the default is.
Saving the DNG from within ACR creates a new version (no way to overwrite), but that saved version grows in file size by roughly the size of the profile file.