Loose fitting power cord.

Another option is to wedge a small wood or similar block under the cord housing to keep it in place

or maybe http://www.furutech.com/2018/05/16/16961/

I've used the electrical tape method as well. If it ever needs to be removed, it can be a sticky mess. Try some heat shrink. 

It will definitely affect sound quality if the power cord falls out.

Its not the outside of the plug but what's inside that's the problem. If the terminals inside the plug grip the pins on the component with enough tension the plug will not fall out no matter how sloppy the fit. Conversely, no matter how much electrical tape you wrap or how tight it stays in nothing like that will address the real problem of the electrical contacts being this weak. 

So you have a piece of crap power cord. Well there are a lot of them out there. Live and learn. The only real fix is replace the plug on the end of the cord. Or you could open it up and try bending the mating parts inside enough to get a better grip.