It looks like a bug. After you run the DTA (Database Tuning Advisor), you cannot synchronize the table without getting errors "Cannot drop the index... because it does not exist".
SQL error description: [Microsoft][SQL Server Native Client 10.0][SQL Server]Cannot drop the index 'LOGISTICSPOSTALADDRESS._dta_index_LOGISTICSPOSTALADDRESS_8_1605632813__K16_K33_K20_K34_K28_K29_1_2_18_19_21_32_', because it does not exist or you do not have permission.
It seems that the DTA creates a lot of 'temporary' indexes to try different scenarios, and even if you never choose to apply these recommendations, AX somehow captures these indexes and will try to drop them with the next synchronization. The problem is these were never created in the first place!! The only workaround I have found is to actually create an index with the same name (it doesn't matter about the fields), then when you run the Sync, it can drop the index and be happy.
It is crazy to produce an error when you can't drop an index that doesn't exist in the first place! Does anyone know where these imaginary indexes are stored? Is there a way to tell AX to not drop indexes that don't exist? How does AX know about the index if it doesn't exist?