The FC mission system seems hosed. I haven't been offered one reliably since Season 3 (IE this issue occurred way back when they launched Season 4.) Bugged it MANY times, but it appears it's either EXTREMELY low priority; or they just have no clue how to correct whatever issues were introduced with Season 4.
Strange. The Diplomatic Investigations and First Contact missions seem to work for me, from the Available Missions tab.
I had my first First Contact mission two weeks ago and haven't been offered another since. Two days ago I made it to Federation Ambassador so I guess it doesn't really matter anymore, but I would have enjoyed obtaining the diplomatic XP by doing First Contact missions instead of delivering commodities all over the galaxy. Delivering goods sounds more like a Trade thing than a Diplomacy thing.