I've noticed on several occasions I was unable to send my fellow mobsters gifts unless I went to their pages, that's when they send me gifts and when they ask for gifts.
Use the Kanoplay site, when accepting and sending gifts and this will not be an issue, as has been stated before this is a FB issue,if indeed you are playing on FB.
I have had the same problem. When I'm helping a player (send boost, or doing out break, ect) The tab comes up to send a gift and when I try to send one I notice at the top of my computer ( the ZS tab) flashes and nothing happens. I also go to their page to send a gift, but the same result.