There could be several causes to this problem, not necessarily obvious either. Firstly, are you attempting to enter the duty as the same class/Job you were when you first accepted the quest? SE changed it that you can't switch classes mid quest to do a duty and get exp on another class, you have to enter the duty with the same class or Job you first initiated the quest as to complete it.

Failing that, are you attempting to enter the duty with your chocobo out? When you have your chocobo companion summoned, the game considers you to be in a 'party', which will prevent you from entering a solo duty (you will have to dismiss your chocobo in order to enter).

Otherwise, if you still can't enter even after that, try clicking on the red exclamation mark above Cid's head - the Journal entry for the duty should mention in red writing overlaying the journal why you can't enter the duty.