There are NO errors, but appointments deleted continue to show in the calendar.

Analysis:

This is a copy of one of your relationship settings:

Conflict Resolution: 1 (Always Replace The Item In The Destination Folder)
Copied Resolution: 1 (Overwrite Changes)
Deleted Destination: 4 (ReCopy The Source Item)
Deleted Source: 2 (Delete Destination Item)

This relationship is set to recopy the item if the destination item is deleted.

To change this to your desired behavior

Log on as the a2e service account

Open the Add2Exchange Console

Locate his relationship(s): Any source to HIS destination

Change the destination item deleted from Recopy to Delete Source or DO Nothing

If you set all relationships up so when the user deletes the destination it will delete the source, it is bidirectional on Deletes.  If you set it up so it has the Do Nothing option, it will delete his destination and never come back again.

If you select the DO nothing option the relationship is still unidirectional and any change or deletion by a user with a copy will have no effect on the source.  If the destination item is deleted, the appointment would not be deleted from the source, but would be deleted from that user and never come back. 

Once you have chosen the appropriate setting for your business need, close the A2E Console and start the Add2Exchange Service

We always suggest telling the affected user of the change in any and all A2E relationships.

TIP:

I noticed you had settings for unidirectional data flow in your relationship. That means the information only flows one way, from source to destination.  In a unidirectional relationship, when a user changes the destination copy, it will not change the source, but if the destination item is deleted, you MAY want the user to be able to delete the source as mentioned in one of the options above.  If this is the case, the resulting relationship would be bidirectional on deletes, but unidirectional on edits.  This kind of relationship is not common, but can be done if you wish. 

Usually if a user has the ability to delete the appointment, the user would ALSO want the ability to edit their copy and have it update the source and through synchronization, change the appointment for all.  If that “editing” capability is desired, change the Conflict resolution to “always overwrite the source” and then change the Copied resolution to “sync changes back to the source” for the desired relationships affecting that user.

Again, if you do not want to grant this editing capability, and just want the appointment to be deleted and never come back to that user, just change the destination item deleted resolution to “Do nothing” and the relationship will still be unidirectional on edits and deletes.

Hope this helps!