First, don't use this expression in a text field with an auto-entered calculation. Use it in a field of type calculation that returns text. In Specify Calculation, there's the button you are looking for. Click Storage Options and specify "do not store".
As an unstored calculation, like most calculations that use a get function, a calculation with Get ( CurrentDate ) will update as time passes. If it is stored, it will not update as you have found out.