Q:

How can I separate an 8H antenna from a modified 1×1 with ring? 

I have two parts which are stuck together:

4081b: Plate, modified 1×1 with clip light – thick ring
2569/25699/47094: Antenna whip 8H

The parts have been assembled like this for about 20 years and may have dust in between them.  They have been cleaned with water and mild hand soap.  They were stuck firmly before cleaning.  Other instances of the same assembly were not so difficult to take apart. 
I have tried gripping the antenna and pushing it through, prying my fingernail against the lip where the antenna gets thicker near the base, and prying between the base and the ring with fingernails.  I've also tried flicking the tip of the antenna to try to knock it loose and twisting while holding the shaft, but it's really in there.  Before I try prying with stronger tools that could gouge the parts, I wonder if anyone has any tricks for separating these parts. 

A:

Ah, yes.  I have had this problem a few times.  Here's what I do:

The first thing you're going to want is leverage.  Connect one 1x6 plate to the underside of the Modified 1x1, one on top of the previous plate (but adjacent to the Modified 1x1), and one on top of both pieces. 

Next, slide propeller piece 32125 over the tip of the antenna. 

Hold the antenna upside-down (vertically), with the 1x6 assembly in your right hand.  Move the propeller piece all the way up, but stop before it gets to the section the Modified 1x1 is on.  Maneuver the antenna's stem into one of the four sides of the axle hole on the propeller piece, tilt it at an angle, and push up.  There should be a slight pop and the 1x1 will move down the antenna. 

Now that you have something to push on, simply remove the propeller, grab hold of the 1x6's with your right hand, and press into the base of the antenna with the propeller piece.  It should pop out the rest of the way and then you're done! 

Why does this work?  Well, the propeller piece is perfect because it had a proper diameter to fit over the round tip, and the sides of the axle hole are a prefect dimension to hold the smaller thickness of the antenna stem, thus giving you a contact point for applying pressure.  I suppose it's a bit over complicated, but it works for me. :) 

A:

I fail to reproduce your problem.  When I combine these parts, they are easily separable.  Hence the following is an educated guess:

Put the antenna on a big plate on a table (for stabilisation). 
Grab the antenna slightly above the clip with one hand and hold it tight. 
Grab the clip with the other hand and push up, while turning it around the antenna’s axis. 
If needed, use the rest of your hands to push down the plate for further stabilisation. 

A:

For completeness, I am posting the solution which ultimately worked for me.  It is just Wrzlprmft's answer with extra parts to keep the 1x1 in place.  It is also very similar to Magnus's answer, but without the propeller. 
I surrounded the 1x1 with blocks on all sides so that it could not rotate or come off easily.  Then I firmly gripped the antenna as close to the base as I could and pushed it through.