If queries are failing (standard or advanced), it could be due to "Standardized queries" being set to false in ArcGIS Server. An example error that is seen on the database side:
Geodatabase error: Underlying DBMS error [[Microsoft][SQL Server Native Client 11.0][SQL Server]Incorrect syntax near '2012-09-04'.] [Arealinformation.DMP.BES_NATURTYPER]
With "Standardized queries" disabled, Essentials required that you explicitly state which data provider that is being used. The administrator can change the Default Data Provider across the whole site or can configure it at the layer level. Once these settings are specified, the queries should be customized to the data provider specified, which should resolve the issue. To apply the default data provider for the whole site, open the site in question and choose the "Site Info" tab. In there, you will see a setting called "Default Data Provider". Erase "Default" and type the appropriate data provider (it will auto-complete). To apply the default data provider at a layer level, edit the layer in question and under the "Details" tab, change "Data Provider" to the appropriate data provider.