Loose fitting power cord.

@noromance
Makes sense, but some of these aftermarket cables make a tight electrical connection. It’s the smaller size of the molded termination that creates wiggle-room in the IEC.
This is the case with my Audience PC’s.

However, the OP's cable seems like it's not a tight connection.

As both millercarbon and me noted above, you need to increase the *electrical* connection. If the male and female parts do not have close contact, you'll have micro-arcing and noise that will negatively impact the sound quality.

Wrap the Teflon plumber’s tape around the termination of the PC. This will make it fatter and will be a tighter fit. I have used this method many times.
If the cable is extremely heavy, I use a block of wood or heavy sponge rubber underneath the cable behind the component.

Electrical tape is the first method I tried and it’s a bitch to clean it all off. No adhesive on Teflon tape and it's resistant to heat.

The only helpful suggestion here was from mc.  The teflon tape belongs around the brass contacts of the IEC so that it electrically, not mechanically, has a tighter grip.

The electrical tape might work, but sounds to me like a perfect excuse to put on the dark, dark goggles and pull out the welding equipment.

Thanks everyone so much for your suggestions!

You could also use an IEC C13 to C14 adapter...

Try bending the male prongs gently outward on the amp with a pliers. This will increase tension on the connection with the female connector on the lead.

Try plumbers Teflon tape. Easy to remove.

What rubbish.  It's perfectly well known that many manufacturers stray slightly from the established standards of external size of plug and internal size of receptacle.  Others have reported the reverse problem, struggling to get a plug all the way in.  In the past I've had problems with Cardas PCs, also being a crap manufacturer, right?

Besides the electrical tape, which I've used successfully, you have also try to improvise something to support the cord near the plug.  The heavier the cord--garden hose variety--the more likely this is to happen.  I know the biggest model of Pangea causes problems.

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. 

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. 

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

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