I am going to feel like Dr. Ruth answering this...
I have a similar problem but in my case is the shear weight of the cable that makes it pull out of the back of my Oppo DVD player. My solution may not be the prettiest but it works. What I did was to "bundle" the HDMI cable with other cables on the back of the player that have firmer connections.

I am not familiar with your television but you could do something like plugging something to the VGA plug (even if it doesn't go anywhere), which can be screwed down tightly, then zip-tie that cable and the HDMI cable together. If your HDMI cable has some firmness to it, this setup should at least keep it pointed in the right direction even if its loose. If you don't have a plug that can be screwed down, just pick whatever is nearby that you know can provide the additional support.

Like I said, not pretty, but I hope it helps.