Another option would be to use arcpy/python. The general code work flow would go something like this:
- Use search cursor against the layer/date field and create a arrary pair list (feature ID, and date) sorted by oldest to newest date.
- For each item in the date list, do another search cursor and grab the shape geometry (array of vertice x/y value pairs) and write the features using an insert cursor to a new or empty template feature class.
In theory this method should write all the features from oldest to newest, which should display the newest features on-top. You could create a script to run this manually or call this script to run via Windows scheduler at x time interval.
Also, you may reference this Q/A for additional options:
Changing order of features in shapefileChanging order of features in shapefile