There are numerous ways in which hands are held in place and sooner or later most types loosen or fail, especially the tapered Pin & Washer method. As a result, the minute hand falls off.

If the minute hand was locked in position it would be impossible to adjust the time without the pendulum swinging frantically to keep up. Most clocks have a friction 'clutch' that allows the minute hand to move independently and the early hand retaining methods were designed to accommodate this arrangement.

More modern ones have threaded nuts in place of the washer & pin. 

There are 12 standard sizes of Clockmaker's tapered pins and numerous sizes and styles of hand washers. Solid turned washers and pressed brass & steel ones, some with round holes and others with square holes. Like so many clock parts, there was no standard to follow so the chances of finding a washer that will fit without adjustment is slim. The same applies to threaded hand nuts.

In addition to the 12 standard sizes of pins, 'Universal pins' exist. They are similarly tapered but much longer. If you only have a couple of clocks to deal with, look out for a 'Universal Pin Kit'. The four types of pin in those kits will suit almost every pin hole in any domestic clock movement.

Repairing Your Own Clocks by Mervyn Passmore