You can try but there is no guarantee.  They will not really care too much about the reasons for the delay since it is very clear that if the application is not submitted in a timely manner, it cannot be reviewed.  You should have submitted it on time even if it meant paying the filing fee which might be a waster after the fact (if you had chosen to get a new F-1 status) but this is not really something USCIS is going to be concerned with.