Make sure the total number of BOffs in your Candidates roster will be less-than-or-equal-to 12 _after_ you collect the BOffs from your mail.
To see your BOff Candidates roster, use the 'u' hotkey to view your toon's status UI screen. Then click on the "Stations" tab, and look along the right side of that UI screen under "Bridge Officer Candidates."
12 is the hard maximum cap you can have in your BOff Candidates roster. As with all mail with attachments, you can only "take items" if your toon has room to hold all of the items attached to the mail.
If this does not explain the issue you are experiencing, you can try looking in your Chat UI screen for error messages when you click on the "take items" button... scratch that. I just tried collecting a BOff from the mail while having a full Candidate roster and I did not get an error message when "take items" button didn't work.
... would be nice if the game gave us a notice akin to "You do not have room for those items". *hint* *hint*
You mentioned BOffs in your first post but then typed duty officer in your last post. Which did you mean?
If we're still talking about BOffs, have you tried making space in your Active Roster (left hand side under the "Status" tab in the status UI screen), and then trying the "take items" button?
To make space in your Active Roster without losing your current BOffs, you have two options that do not include using the Mail system:
1) Put them up on the exchange for a large sum of ECs (10Mil for Silver players without the EC Cap upgrade or larger if you are Gold/Lifetime/have the EC Cap upgrade)
2) Trade them to a friend who has room to hold them in their Active Roster (who, of course, will be able and willing to trade them back to you when you are done)
Before attempting one of the above 2 options, you will need to empty your BOffs of all equipment and items. The game will not allow trading of BOffs who are equip'd in any way for fear they they are carrying anything that is bound-to-account/player. Also, there is a very small chance someone may buy your BOffs off the exchange if you go that route... highly unlikely, but still possible.
Switching topics here... if you really meant DOffs, we can take the conversation down that road.