Thanks for the reply, Raze!
So, I can exactly tell you what happens:
I'm player one, my gf is player two.
During our playthrough suddenly I couldn't use "X" on stuff in containers anymore, This included stuff in the purse of an NPC which I stole. The context menu is visible for a split second (I think around 1/30 of a second or so) and then disappears. It doesn't matter what item type I try to open the context menu on.
Restarting the game, even restarting the PC, didn't help. Suddenly, after a few hours, the context menu worked again. I was unable to reproduce the problem afterwards. I tried using a different USB port, nothing helped. My gf did NOT have the same problem with her controller.
I will make a savegame when I get this again and send it to you if that is ok?