The issue that you need to combat when it comes to online shoppers is that online shoppers tend to be procrastinators, they will wait until your final ship day to pull the trigger. The problem here is that every day you do not close this person, you stand a greater chance of never closing them.
Try and timed-promotion. Put on your site “Free Shipping untl this Sunday” or “Inventory wont last, order by Sunday” come up with a promotion with a very fixed date and continue to refresh it. Sometimes it only requires a small push to get them to turn into a buyer.