Yes, that is the little mm plastic part I was talking about as well.
If you still have some of the now old fashioned plastic model kits or other thermoplastic plastics: Take a sprue and heat it with a lighter till it melts. Then you can pull on both ends till you have the desired diameter (0.6 mm (?) Let it cool down, and with a scalpel you can cut off a slide from 0.2mm. You can glue that in position between the physical button and the actual contact on the flex cable with a cyano acrylate glue.
Job done! :-)