Active Directory Security Group “Work E-Mail” not syncing

Question

Here is what I'm doing:

1. I have an Active Directory Security Group and a SharePoint Group
2. I add the Security Group as a member of my SharePoint Group
3. The Security Group is added to the list of groups for the site collection
4. The Security Group is NOT e-mail enabled so the "Work e-mail" field is empty
5. I update the Security Group to be e-mail enabled

At this point the Security Group still does not have a value for the "Work e-mail" field. I then try running full user profile synchronization but the "Work e-mail" field does not update. I try stsadm deleteolddatabases and then run the sync and it still doesn't update.

I know that I can manually delete the Security Group and then re-add it to the SharePoint Group but I don't want to have to remember to do that everyone time that there is an update to a security group. Is there a way to automate this?