The theory is that as DW has no minerals dissolved in it, it will more aggressively dissolve any soluble minerals on the coin. This extra disolveabilty stops working when the water is saturated with minerals, so as a rule of thumb I change the water every day for the first week or so, then leave for longer and longer periods.... You can generally judge how often you need to change the water by the condition of the coin....
If the crud is softening up overnight you probably want to change the water... If its remaining rock hard, not so much.