<snip>
(those commands should run the cron normally except starting at 03:00, where it should kick off at 3:15 instead of 03:05)
If it also fails to start at 03:15 then that would suggest that something is happening to the cron job the last time it is run to make it hang (or make the system think it is hung).
I wonder if the other end has some file(s) locked for writing or other reason and that is choking the local wget.