It is because your function on triggered with keyup event it making the browser gag, I do not have the time to check the whole function, but you should look into it.
As a quick fix, do not set timeout for blockui, and add a delay in calling keyup, like this:
$.blockUI({message: '<h3>Loading</h3>'});
setTimeout(function(){$('.modx').val('').trigger('keyup');},500);
Than at the end of keyup function just add a call to release the blocked ui, like this:
$.unblockUI();
See the full fiddle here, but please I will like to STRETCH out this is just a patch, to get it working you should really sort out your function which causes the halt.
Emil