Blur event stops click event from working?

click event triggers after the blur so the link gets hidden. Instead of click use mousedown it will work.

$('.ShippingGroupLinkList').live("mousedown", function(e) {
    alert('You wont see me if your cursor was in the text box');
});

Other alternative is to have some delay before you hide the links on blur event. Its upto you which approach to go for.

Demo

You could try the mousedown event instead of click.

$('.ShippingGroupLinkList').live("mousedown", function(e) {
    alert('You wont see me if your cursor was in the text box');
});

This is clearly not the best solution as a mousedown event is not achieved the same way for the user than a click event. Unfortunately, the blur event will cancel out mouseup events as well.