This is the mistake you are making,last due date is not for cheque to be dropped but payment to be recieved so u need to ensure that you drop the cheque atleast 2-4 days earlier. if you have a problem then right the date on the cheque as the due date only so that it gets cleared only on due date. Take my advice i m sure it works. I have worked for a MNC bank that is why i know this:)
