Cloth simulation doesn't work for particular object

I had the same problem. Took me over half an hour to figure out.

The problem is caused by duplicated vertices.

To fix it switch to edit mode. Press Alt + H to make sure there is nothing hidden. Then select all vertices A and then press M to merge them by distance.

Have a look at the status bar: 148 vertices removed. Switch back to object mode. Play the simulation. It works again.

You might want to double check the physics propteries of the object. Also you may want to try duplicating the object, or restarting blender. Also, and I'm not sure about this, but if your object is instanced it may not be possible. Check the data and see if it's in use by more than one object.

Pressing playback is not a good way to review the cloth simulation. You need to let the computer calculate the equations and mathematical things for the cloth so that you can see them correctly. You do this for the first time only and then you will be able to playback because the baking process results can be saved on your hard drive.

How to bake cloth simulation:

1. Select your cloth in object mode.
2. Go to the physics settings (By clicking on the physics tab).
3. Expand the "Cache" section.
4. Set the frames where you need to start and end your simulation.
5. (Optional) uncheck "Use Library Path" and check "External" to save it in a specific or known location on your hard drive.
6. Click on Bake button and let your computer take its time.

Further work:

What if you don't like to edit your cloth after you baked it? You can simply click on "Free bake" then, you can edit your mesh (cloth) and then rebake using the previous steps.