The loyalty mission is triggered after completing a certain number of missions (1 or 2 depending on who was your most recent squadmate)
Have you completed all the Assignments too? If not, completing them also contributes toward this mission count.
If you did complete them, I would suggest
a) tweaking with Gibbed Save Editor (if you're on PC)
-First, download it (http://social.biowar...m/project/4373/)
-Then, open the Gibbed Save Editor
-Click open (The folder, second button on the upper left corner)
-Open your SaveGame Folder (Shows your Character Name, the Level, The Class and the Date it was last played, for example John_23_Infiltrator_140715 )
-Then, open the most recent save you have
-Go to Plot. then Henchmen.
-Check the Plot Mark "Thane's Alternate Appearence acquired.
-Then, save your modifications into the save you're tweaking with. Overwrite your save.
-Load the save in-game.
-Thane's Loyalty mission will appear in your Journal
B- If you're not on PC, the only solution is loading a previous save where you still didn't complete all the missions.
c) The other alternative is doing it after the Suicide Mission. Your whole squad can still live if you just have Thane Unloyal. Just don't pick him as a team-mate in the base and you should be fine.
Edit: Actually, Shadow Broker DLC can be completed anytime you want, there are just some dialogue changes if you do it after the Suicide Mission, but nothing that can't be found on Youtube.