When I loaded your game, pirates showed up at Endilean 2 and a few months later on 2240.12.27 I saw a hidden pirate base pop up at 11%. By 2241.04.05, it was at 80% and it finished on 2241.05.05. So around 4 1/2 months game time to build - which goes fairly quickly at 2x speed.
Perhaps there's a faster build time due to difficulty level. You mentioned you were playing on very hard, but your game appears to be on extreme difficulty. It shows that in the empire comparison screen, plus I did a quick check of two comparable planets (one of yours, one of another empire), and they get around 4x the GDP that you are (which is what I see in my games at that difficulty level).
Also, those are Ugnari pirates, and maybe that race's 20% construction speed bonus is applied to facility construction, although someone else would have to verify that.
I don't see anything different from what happens in my games, although I tend to play at a slower speed. Even then, if I'm distracted, I'll check my colony screen and see a new base fully built (especially when I'm micromanaging space battles). Maybe a dev will take a look and can give you a more informed opinion. Until then I'd suggest doing more to stamp out pirate bases in your area. I tend to build gas mining stations at all fuel locations so they don't sneak in and start building w/o me being aware of it. Or if you add a few basic weapons to your outpost design, you have a cheap base that you can probably get up at colonies easy enough that can shoo off the lone pirate or two for the same expense as a single troop, giving you not only those med/rec bonuses but preventing a small force from gaining enough influence to start building a hidden pirate base facility in the first place.
< Message edited by Vardis -- 8/8/2014 12:32:36 AM >