Oh my PS4 does this sometimes too! (but then it will start working for like 6 months before it happens again)

From what I can tell it might have something to do with the temperature of the room making the plastic expand ever so slightly. They made the eject button WAAAAY too sensitive on the PS4, it only needs to be pushed like half a millimetre and it will eject.

My solution is similar to yours, I would usually unplug it and move it around. I also found if I left the front right corner of the PS4 hanging off the edge of my entertainment unit it would stop doing it.

Now that I think about it, it probably hasn't done it in a year or so now. Needless to say I never move the thing just in case haha.