How do I keep my swivel recliner from swiveling when I don't want it to?
 

First-world problems! :)

My knees start hurting, so I put up the footrest, and it immediately drifts to one side or another. I reach out and straighten my recliner, only to have it immediately drift again.
I don't want to disable it completely, I needed to climb over the side of my old recliner.
I don't want to go back!
I keep visualizing some kind of hand brake... for a recliner! :D

Magnets!

Don't provide lateral input.

A hook in the ceiling directly above the chair ....with a trapeze.

Scrap towel around the swivel

Nah too simple, need rube goldberg device

How about a heavy gyro on the upper part?

Riffing on the heavy gyro theme: vacuum powered sperry gyro out of a spitfire running a case tractor engine powered hydraulic ram with steam powered position actuators.

Tesla turbine with a flapper valve to opposed inlet jets.

You could just blow into a tube. :)