There can be several reasons for this.
You should have a good grease and maitenence program for your equipment, aside from this issue. Hopefully you are doing so. If lack of grease is causing this problem, you are going to have many more issues down the road.
There are parts on the tractor - it is 60 or more years old - that wear down over time and use. Shafts wobble a bit, the hand lever wobbles a bit, as holes wear bigger. Some of the parts connected to the pto lever can just be worn down, and no longer catch and hold where they should, allowing things to slip apart.
It sounds like you are not so very mechanically inclined, so it may be difficult to get a quick and easy explanation? It is a process to go through and check stuff, eliminate some of the reasons, and focus on the more likely worn, loose, or stiff parts that cause this.
I know I'm not answering your question exactly, but hopefully this starts you down the road, and can work through it to find the real cause of the problem.