Stop doing work. Now. You need to cut your losses. I would even limit the amount of time you spend communicating to the customer. They need to understand that everything is cut off and the project abandoned (unless they pay up).
If they are not paying at 30%, they won't pay at 100%. (Either because they don't want to, because you're not good enough, or just because of lack of communication.) It doesn't matter why. This milestone allows you to cut nonpaying clients (or for clients that feel obligated to pay, to cut nonperforming contractors).
Next time request a deposit (even 10% will make the client feel more invested) or have a 10-20% milestone that is for conceptual design. Also think about being more client selective. Really, I think the deposit is the thing to do to weed out non-serious customers.
Also, while you should ideally strategize to avoid/limit non-payment, you will have some. So price your services accordingly-, therefore, price your services accordingly -this this is unfortunate for the paying customers but is unavoidable.