Temple of the Exalted, Moon programme and Tobias’ fortress constructions keep getting stuck. I’m at a loss as to how this is fixed or broken as sometimes, usually at the end of the week or 3 day cycle, construction suddenly resumes, only to get stuck again the next time I go on a mission or something. Has anyone encountered this before?
Didn’t think about it before seeing your post, I just thought it took them a really really long time to complete it, but after checking up on some older save games I can see that it is indeed stuck in my game too.
I checked three different in-game dates, and the progression on the Moon Launch Site was as follows:
19/2 3d 0%
21/2 2d 26%
23/2 2d 26%
So yeah, looks like it’s stuck for me too 
It progress slowly and information is not updated in real time. If faction has disabled research zones then their faction unique building construction is stopped. You need to pay attention when aliens try to destroy havens with research centers and prevent that.
If faction will loose all havens with research zones then their will never finish that building.
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Do you mean that if they have just a single disabled research facility in ANY of their havens, then the construction of the Moon Launch Site will be halted? 'cause I can see they still have plenty of active research facilities spread out around their havens, but I can’t say for sure if ONE of them is damaged atm.
I love this game so much, but damn it would be nice if it actually gave you all the info you needed. Stuff like this just feels like a bug, even if it might be working as intended, if you’re not informed about the underlying mechanics 
If they have some active - non damaged research zones construction should progress. It may be just really slow.
Yeah I wish that many game mechanics would be better explained somewhere in the UI. There are still many questions about some things that no one knows, except developers.
That’s not the case for me, it is completely stuck, not just slow.