The description of the Algurnir Axe (from the Twilight Pack) makes it clear that its own perk will only work if it's in the main hand, and no other items are equipped in the secondary hand.
However, the bug is that if you have something else equipped in the secondary hand, instead of only be the Alguirnir's perk not working, ALL perks including those from the bow and secondary-item (be it another weapon or shield) will suddenly not work.
You can witness this in the video by looking at the symbols above my adrenaline bar.