We have recently upgraded to Moodle 2.4.2 and we are slowly but surely working everything out. Here is a weird one. If the length of the assignment name is too long you can't duplicate the assignment using the duplicate icon. If you try, it actually says that it was duplicated but if you click return to course it won't be there and if you click edit new copy it will give you a course module id error. I have not whittled my experiment down to determine the exact string length of characters that the assignment name needs to be under.
Length of Assignment Name Problem
Interesting, before I started using CSS and now have titles of 25 characters, I used to use HTML that added about 70 characters making my titles 80-90 characters in length. Although this causes strange situations in column names and e-mail messages, I have never had a problem with duplication of an assignment.
I mention this just to help you keep looking in case the problem may not be based on title length.
How many characters are you trying to use?
Sorry, I didn't get back to this earlier. I have whittled it down and it's weird. If I use 31 characters or less in the title I can duplicate it. If more than 31 I cannot. We are having a real tough time working out backup issues and I have a feeling this has to be part of that.