Most of you probably wont know the answer to this, with your modern washers.
Anyhow, I bought an old Maytag Wringer washer to wash greasy rags from the garage, or wash things like horse blankets.
The funny thing is that I have found I like using it a lot more than my modern washer. First off, I'm more in control of it, and if I have very filthy pants, I control how long they wash, and I can easily rinse them more than once. Secondly, every modern washer I have ever owned seems to have a habit of 'eating' a piece of clothing every so often. The wringer machine has never done that.
So, I do almost all laundry in that wringer machine now.
The machine is at last 50 years old and works great, except for one thing. Every so often, the agitator pops off the shaft while its washing. I take it off after almost every load of laundry so I can wash the dirt off the bottom of the machine, and I always put it back on firmly and even bang it downward with my fist each time. But it still pops off far too often.
It seems to me that I once heard there is supposed to be a rubber O-ring inside the bottom of the agitator hole, where it goes on the shaft, and there is a groove in there which could accomodate such a ring. But getting parts is near impossible anymore. I've called several appliance stores that advertise "Maytag" and they just tell me that they no longer have parts, or one of them told me that no one uses wringer washers anymore.
My point in posting this is because maybe someone of you still has one of these machines. If you do, could you look and see if there is a O-ring and maybe post a photo of it on some "post your photos" website.
Otherwise, I'm pretty much at the mercy of buying a complete assortment of O-rings and just trying to find one that works.....
The only other thing I can think of, would be to put a few wraps of electrical tape around the splined shaft, and will probably have to replace it every few weeks. My other thought was to brush on some rubber cement, and let it dry before putting the agitator back. But that too will probably have to be replaced often.