UP3214Q/UP2414Q - 1/2 screen issue and/or No picture after powering off, then on

I got some more problems with the UP3214Q: Every couple of computer starts, once I get the login screen displayed, only half the screen shows a picture (the right hand side), with the left half being black. After login, I get the full picture. Prior to the login screen, I also have full screen picture (BIOS screen, Windows loading screen). The second issue is even more annoying: If I power off the device while my PC is still running, then power it back on, I will never get a picture again. No amount of hitting random keys and klicking about (I can hear windows and moan in the background If I manage to blindly hit the wrong option) will get back any picture. Neither will switching to another input then back, nor will unplugging the displayport cable from the machine, or putting the machine to sleep and returning it back from sleep. The only way to get the picture back is to shut down the shut down the machine completely, then boot it up again. Is this supposed to happen or is something wrong with my display?