For most people, the 60 days start from the completion date on their I-20. If you graduated earlier than the I-20 date, the 60 days start from the date of completion of your program of study.

Besides the 12 months full-time CPT and pre-completion OPT I can't think of any reason your OPT would be denied. I have heard of a guy whose OPT extension was denied because the school put the wrong CIP code. It could be a similar clerical error that got your request rejected. Please post the reason once you get the letter. It will be helpful to all.